Paul Milgrom - Knowledge

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recently granted to Diamond, Mortensen and Pissarides (DMP). Shimer explained that in the standard DMP model, a shock that raises the value of what firms sell – other things the same – increases their incentive to hire workers by raising profits per worker. The problem, according to Shimer is that this mechanism sets into motion a negative feedback loop which in the end largely cancels firms' incentive to expand employment. In particular, as employment expands, labor market conditions in general begin to improve for workers and this puts them in a stronger position as they negotiate wages with employers. But, the resulting rise in the wage then cuts into the profits earned by firms and thus limits their incentive to hire workers. The problem has come to be known as the 'Shimer puzzle'. That puzzle can loosely be paraphrased as follows: "what modification to the DMP framework is needed to put it in line with the empirical evidence that employment rises sharply during a business cycle expansion?" Although enormous efforts have been made, the puzzle has largely resisted a solution, until the Milgrom paper. Milgrom (with Hall), argued that the bargaining framework used in the standard DMP model does not correspond well to the way wages are actually negotiated. They argue that, by the time workers and firms sit down to bargain, they know that there is a substantial amount to be gained if they make a deal. The firm's human resources department has most likely already checked out the worker to verify that they are suitable. Most likely, the worker has done a similar preliminary check to verify that they could make a useful contribution to the firm. A consequence of this is that if, during the negotiations, the firm and worker disagree, they are very unlikely to simply part ways. Instead, it is more likely that they continue negotiating until they do reach agreement. It follows that as they make proposals and counterproposals, bargaining worker/firm pairs are mindful of the various costs associated with delay and the making of counterproposals. They are not so concerned about the consequences of a total breakdown in negotiations and of having to go back to the general labor market to search for another worker or job. Milgrom stresses that with this shift in perspective on bargaining, the impact of improved general conditions on the wage bargain is weakened as long as costs of delay and renegotiation are not very sensitive to broader economic conditions. In particular, the approach provides a potential resolution to the Shimer puzzle, a puzzle that has confounded macroeconomists generally.

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single task, a principal can either reward performance (or some measure of it) or change the agent's opportunity cost of performing that task. This second strategy is key to understanding what happens when an agent has more than one task to which he can allocate effort, because increasing the reward on one task will generally alter the agent's opportunity cost of allocating effort to other tasks, increasing it when the tasks are substitutes for the agent and decreasing it when the tasks are complements. Holmstrom and Milgrom's (1991) paper demonstrates that when tasks are substitutes for the agent and it is difficult to measure performance on one of them, it may be optimal to have low-powered incentives, or even no incentives, on all tasks, even if some can be easily measured. They also demonstrated that the difficulties of providing incentives on multiple tasks have implications for the design of jobs. For instance, it may be better to split conflicting tasks between agents or to vary the intensity of monitoring and communication. Finally, in their 1994 paper, Holmstrom and Milgrom broadened the scope of their analysis to include not only performance-related pay but also other management choices that affect agents' incentives, such as choices about how much discretion to give agents and about whether or not agents own the assets with which they work. This paper stressed the interactions (the "complementarities") between these different choices, showing that the optimal choices for the principal will often vary together as the contracting environment changes. Holmstrom recounted the impact of this work at the Nemmers Conference in Honor of Paul Milgrom.

1192:, applied a repeated game model to explain the role of merchant guilds in the medieval period (Greif, Milgrom and Weingast, 1994). The paper beings with the observation that long-distance trade in the somewhat chaotic environment of the Middle Ages exposed traveling merchants to the risk of attack, confiscation of goods and unenforced agreements. Merchants thus required the assistance of local rulers for protection of person, property and contract. But what reason did rulers have to provide this assistance? A key insight from the paper is that neither bilateral nor multilateral reputation mechanisms can support the incentives of a ruler to protect foreign merchants as trade reaches an efficient level. The reason is that at the efficient level the marginal value of losing the trade of a single or even a subset of merchants—in their attempt to punish a defaulting ruler—approaches zero. The threat is, thus, insufficient to deter a ruler from confiscating goods or to encourage their expenditure of resources or political capital to defend foreign merchants against local citizens. Effective punishment that will deter rulers' bad behavior requires more extensive coordination of effectively all the merchants who provide value for the ruler. The question then becomes, what incentives do the merchants have to participate in the collective boycott? Here is the role for the Merchant 1236:"Why do traders bother to gather information if they cannot profit from it? How does information come to be reflected in prices if informed traders do not trade or if they ignore their private information in making inferences?" These questions, asked at the end of Milgrom and Stokey (1982), were addressed in Glosten and Milgrom (1985). In this seminal paper, the authors provided a dynamic model of the price formation process in securities markets and an information-based explanation for the spread between the bid and ask prices. Because informed traders have better information than market-makers, market-makers incur a loss when trading with informed traders. Market-makers use the bid-ask spread to recoup this loss from uninformed traders, who have private reasons for trading, for example, because of liquidity needs. This dynamic trading model with asymmetric information has been one of the workhorse models in the literature on market microstructure. 978:, asked what features of a contracting problem would give rise to a simpler, say, linear, incentive scheme (that is, a scheme in which the wage consisted of a base amount plus amounts that were directly proportional to specific performance measures). Previously, most theoretical papers in agency theory assumed that the main problem was to provide an incentive for an agent to exert more effort on just one activity. But in many situations, agents can actually exert unobservable efforts on several different activities. In such contexts, new kinds of incentive problems can arise, since giving an agent more incentive to exert effort on one dimension could cause the agent to neglect other important dimensions. Holmstrom and Milgrom believed that incorporating this multi-dimensional feature of incentive problems would generate implications for optimal incentive design that were more relevant for real world contracting problems. 1211:

notion that adversarial litigation will lead to the truth is true if the parties are symmetrically informed and both have access to verifiable evidence that demonstrates the truth and so long as one of the parties prefers the decision that even a naive decisionmaker (who chooses from a set of decisions suggested by the parties) will reach under full information to the alternative under partial information. They also show, building on Milgrom (1981c) and Grossman (1981) that a decisionmaker can induce parties with less than complete information to reveal enough to ultimately result in full revelation by adopting a skeptical posture, drawing sufficiently negative inferences from weak or non-existent evidentiary showings. This early model laid the groundwork for future work on strategic information behavior in courts Shin (1998) and Daughter and

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incentives to spend time attempting to influence the outcomes. Since this time could instead be spent on productive tasks, influence activities are costly for the firm. Milgrom shows that firms may limit the discretion of managers in order to avoid these costs (Milgrom, 1988). In a paper with John Roberts, Milgrom also studied a model in which employees have information that is valuable to the decision maker. As a result, allowing some degree of influence is beneficial, but excessive influence is costly. Milgrom and Roberts compare various strategies that firms might use to discourage excessive influence activities, and they show that typically, limiting employees' access to decision makers and altering decision-making criteria are preferable to the use of explicit financial incentives (Milgrom and Roberts, 1988). In another paper, with

1290:(FCC) has responsibility for allocating licenses for the use of electromagnetic spectrum to television broadcasters, mobile wireless services providers, satellite service providers, and others. Prior to 1993, the FCC's authorization from the U.S. Congress only allowed it to allocate licenses through an administrative process referred to as "comparative hearings" or by holding a lottery. Comparative hearings were extremely time-consuming and costly, and there were concerns about the ability of such a process to identify the 'best' owners for licenses. Lotteries were fast, but clearly a random allocation of licenses left much to be desired in terms of efficiency. Neither of these methods offered any ability for the FCC to capture some of the value of the spectrum licenses for the U.S. taxpayers. 1147:

idea is that, in addition to the prey, the predator too suffers from predatory pricing. If the prey resists predation and remains active, then the predator eventually will give up its efforts. Anticipating this outcome, the prey is indeed better off by resisting predatory efforts. Anticipating this outcome, in turn, the alleged predator is better off by refraining from its predatory strategy. Even if the alleged prey were short of cash, it could always borrow from a bank with the (correct) promise that its losses are only temporary. Further, supposing the predation were successful in inducing exit, if the predator subsequently raised prices to enjoy the fruits of its victory, new entry could be attracted, and the problem starts all over.

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for sale), or persuasive (as for example many television commercials which seem to provide little or no information about a product's characteristics). Following earlier ideas by Nelson (1970, 1974), Milgrom and Roberts (1986) show that even "uninformative" advertising, that is, advertising expenditures that provide no direct information about a product's characteristics, may be informative in equilibrium to the extent that they work as a signal of the advertiser's quality level. Methodologically, Milgrom and Roberts (1986) also make an important contribution: the study of signaling equilibria when the informed party has more than one available signal (price and advertising, in the present case).

1123:. The book covers a wide range of topics in the theory of organizations using modern economic theory. It is Milgrom's most cited work, a remarkable fact, given that it is a textbook aimed at undergraduates and masters students, while Milgrom has so many highly influential, widely cited research papers. In addition to discussing incentive design and complementarities, the book discusses some of the inefficiencies that can arise in large organizations, including the problem of lobbying or "influence costs." In the 2008 Nemmers Prize conference, Roberts commented that the impact of the work on influence on management scholarship had exceeded its impact on economic scholarship. 1107:'s performance incentive system because the classic piece rate contract was supported by a string of human resource policies (e.g., subjective bonuses, lifetime employment) as well as production management policies (including organizational slack on delivery), and, perhaps most importantly, deep trust between workers and management. Thus, successful replication would require getting all of these elements in place. Milgrom and Roberts used the same theory to forecast the difficulties Japanese businesses would have in adjusting to change in the decade and a half following the recession that began in the early 1990s; a prediction that was borne out by subsequent experience. 1326:

simultaneous closing rule to ensure that bidders could not hold back while observing the bids of others. The activity rule required that bidders maintain a certain level of activity, either by being the current high bidder or by submitting a new bid, in each round or else forfeit all or part of its eligibility to submit bids in future rounds. "Milgrom and Weber developed this insight into the activity rule that the FCC has used in all its simultaneous multiple round auctions. The Milgrom-Wilson activity rule was an elegant, novel solution to a difficult practical auction design issue." Activity rules are now common in dynamic multi-item auctions.

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repeated game, assumed to be a prisoners' dilemma, where cheating is the dominant strategy and the only incentive not to cheat is because future partners can learn of this and cheating a cheater is not punishable; this makes the equilibrium sub-game perfect. Understanding the merchants' incentives to create an institution to support decentralized contract enforcement like this helps to overcome the tendency in the law and economics and positive political theory literatures to assume that the role of law is exclusively attributable to the capacity to take advantage of centralized enforcement mechanisms such as state courts and police power.

1215:(2000) relax the symmetry assumption, for example, looking at the impact of sequential evidentiary search decisions or Bayesian inference by judges; Froeb and Kobayashi (1996) and Farmer and Pecorino (2000) investigate the role of evidentiary costs and alternative models of judicial inference; Che and Severinov (2009) explore a role for lawyers who are better informed about the legal significance of evidence and can advise their clients about to reveal in court. This important literature sheds light on the impact of legal rules governing discovery and attorney-client privilege as well as the function of lawyers in adjudicatory systems. 1393:

themselves, or by the political process. Moreover, rational choice approaches to policy evaluation typically assume people will act in a way that maximizes these preferences – this is the justification for leaving choices in the hands of individuals whenever possible. Often, it is precisely these simplifications – that preferences are fundamental, focused on outcomes, and not too easily influenced by one's environment and that people are generally to reason through choices and act according to their preferences – that allow economic analysis to yield sharp answers to a broad range of interesting public policy questions.

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agent (e.g. the salesperson). The unraveling result has implications for a wide variety of situations in which individuals can strategically choose whether to conceal information, but in which lying carries substantial penalties. These situations include courtroom battles, regulation of product testing, and financial disclosure. Milgrom's persuasion game has been hugely influential in the study of financial accounting as a tool for understanding the strategic response of management to changes in disclosure regulation. This work has led to a large literature on strategic communication and information revelation.

1387:... it is worth emphasizing that despite the shortcomings of the rational choice model, it remains a remarkably powerful tool for policy analysis. To see why, imagine conducting a welfare analysis of alternative policies. Under the rational choice approach, one would begin by specifying the relevant preferences over economic outcomes (e.g. everyone likes to consume more, some people might not like inequality, and so on), then model the allocation of resources under alternative policies and finally compare policies by looking at preferences over the alternative outcomes. 1061:

reveals it.) Milgrom demonstrates that, with substantial generality, at every sequential equilibrium of the sales encounter game, the salesperson employs a strategy of full disclosure. This result has come to be known as the "unraveling result," because Milgrom shows that, in any candidate equilibrium in which the buyer expects the salesperson to conceal some observations, the salesperson will have an incentive to reveal the most favorable (to himself) of those observations---thus, any strategy of concealment will "unravel". In a subsequent paper (1986), Milgrom and

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to channels in a way that frees up a contiguous block of spectrum to be repurposed for wireless broadband, with licenses sold to telecommunications firms. Relative to prior spectrum auctions run in the United States and around the world, the incentive auctions will have the novel feature that they are a double auction: the proceeds from selling wireless broadband licenses will be used to compensate broadcasters who relinquish rights, or who must be re-located to new channels. Any further revenue will go to the Treasury.

676:), Milgrom showed that if one or both players have even a very small probability of being committed to playing tit-for-tat, then in equilibrium both players cooperate until the last few periods. This is because even an uncommitted player has an incentive to "build a reputation" for being committed to tit-for-tat, as doing so makes the other player want to cooperate. The Kreps-Milgrom-Roberts-Wilson "Gang of Four" paper launched an entire branch of the game theory literature on such "reputation effects." 915:. ... these results suggest that comparative statics conclusions obtained in models with special simplifying assumptions can often be significantly generalized. The theorems help to distinguish the critical assumptions of an analysis from the other assumptions that simplify calculations but do not alter the qualitative comparative statics conclusions. In that way, the theorems improve our ability to develop useful models of parts of the economy and to interpret those models accurately. 605:

research in industrial organization includes influential studies on limit pricing, entry deterrence, predation, and advertising. In addition, Milgrom has added important novel insights to finance, particularly in connection to speculative trading and market micro-structure. The common theme of his works on auctions, industrial strategies, and financial markets is that economic actors infer from prices and other observables information about the fundamental market values.

990:, contingent on observing the whole history of the process. Under some assumptions on the agent's utility function, it is shown that the optimal compensation scheme for the principal specifies a payment to the agent that is a linear function of the time-aggregates of the performance measures. Such a linear compensation scheme imposes a "uniform incentive pressure" on the agent, leading him to choose a constant drift for each dimension of the Brownian process. 1399:

much smaller contextual details. Moreover, even if people have well-defined preferences, they may not act to maximize them. A crucial question then is whether an alternative model - for example an extension of the rational choice framework that incorporates some of these realistic features – would be a better tool for policy analysis. Developing equally powerful alternatives is an important unresolved question for future generations of economists.

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more complex objects among users, such as landing slots and radio frequencies. In response, Milgrom and Wilson invented new formats for auctioning off many interrelated objects simultaneously, on behalf of a seller motivated by broad societal benefit rather than maximal revenue. In 1994, the US authorities first used one of their auction formats to sell radio frequencies to telecom operators. Since then, many other countries have followed suit.

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uninformed agents (e.g., an entrant) hold about the type of an informed agent (e.g., an incumbent). Suppose that, with some small probability, an incumbent may be "irrational" to the point of always fighting entry (even if this is not a profit maximizing reaction to entry). In this context, by repeatedly fighting rivals with low prices, a predator increases its reputation for "toughness"; and thus encourages exit and discourages future entry.

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closely related, there would be a lower threat of layoffs, because reassignment of workers could occur instead. Similarly, if the unit were independent, there would many fewer opportunities to misrepresent its prospects. These arguments help explain why divestitures of underperforming units occur so frequently and why, when such units do not become stand-alone firms, they are often purchased by buyers operating in related lines of business.

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found that, in a competitive equilibrium, such invisibility could be profitable for firms. This led to less pay to disadvantaged workers in lower-level positions even when they otherwise had the same education and ability as their more advantaged co-workers. Not surprisingly, the returns to investing in education and human capital were reduced for those in disadvantaged groups; reinforcing discriminatory outcomes in labor markets.

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target's long term prospects from entry. Like Milgrom and Roberts (1982a), this paper brought formal understanding to an old idea in industrial organization, this time the concept of limit pricing. In the process of doing so, the paper also uncovered new results of interest. In particular, Milgrom and Roberts (1982b) show that the equilibrium entry rate may actually increase when asymmetric information is introduced.

633:. The Royal Swedish Academy of Sciences stated that it awarded the Nobel Memorial Prize jointly to Milgrom and Wilson because they "used their insights to design new auction formats for goods and services that are difficult to sell in a traditional way, such as radio frequencies. Their discoveries have benefitted sellers, buyers and taxpayers around the world." The citation went on to say: 1455:

implementation of this new Congressional mandate will be guided by the economics, and will seek to maximize the opportunity to unleash investment and innovation, benefit consumers, drive economic growth, and enhance our global competitiveness. The knowledge and experience of this team will complement the substantial expertise of agency staff to meet these goals.

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Northwestern. Milgrom's work on auctions helped lay the groundwork for one of the most fruitful research areas in microeconomics over the last 30 years. His work on the theory of the firm has been equally influential. Milgrom has also made important contributions to the study of how asymmetric information can affect firm behavior in oligopolistic markets.

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certainly can help determine the magnitude of comparative statics effects. But with economic knowledge at its current state, functional form assumptions are never really convincing, and this lends importance to the question I ask and to its answer: One can indeed often draw valid general comparative statics inferences from special cases.

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formulated turned out to be a convex maximization problem, so the solutions were end points, not interior optima where first derivatives were zero. So the Hicks-Samuelson methods for comparative statics were not applicable. Yet they got rich comparative statics results. This led Milgrom to recall the work of Topkis (1968), particularly

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player to others. This is a way to punish a potential deviator without reducing the total future payoffs. The classical folk theorem result under imperfect monitoring is built on this idea. The second general method is to delay the release of information. Under the second method, the outcomes of the noisy signals are released in every

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Milgrom's role in creating it was celebrated again by the prestigious National Academy of Sciences (Beyond Discovery), which is the main scientific advisor to the US government. The SMR design has been copied and adapted worldwide for auctions of radio spectrum, electricity, natural gas, etc. involving hundreds of billion dollars.

1313:"promised to provide much of the operational simplicity of sealed-bid auctions with the economic efficiency of an ascending auction." Milgrom argued successfully for a simultaneous closing rule, as opposed to a market-by-market closing rule advocated by others because the latter might foreclose efficient backup strategies. 813:

sophisticated learners. Thus, a sequence consistent with adaptive learning is also consistent with sophisticated learning. Sophisticated learning allows players to make use of payoff information that is used in equilibrium analysis but does not impose the fulfilled expectations requirement of equilibrium analysis.

1375:, Milgrom taught the first graduate course on Market Design, which brought together topics on auctions, matching, and other related areas. The market design course has served as a basis for many similar graduate courses across the US and around the world, and has helped jump-start the field of Market Design. 1408:

Milgrom has been involved for at least two decades in the design and practice of large-scale auctions. Working with Bob Wilson on behalf of Pacific Bell, he proposed the simultaneous multiple round auction that was adopted by the FCC to run the initial auctions for radio spectrum in the 1990s. He has

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Many of the "objectionable" simplifying features of the rational choice model combine to make such an analysis feasible. By taking preferences over economic outcomes as the starting point, the approach abstracts from the idea that preferences might be influenced by contextual details, by the policies

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In 2012, the US Congress authorized the FCC to conduct the first spectrum incentive auctions. As envisioned by the FCC, the incentive auctions will enable television broadcast stations to submit bids to relinquish existing spectrum rights. Broadcast stations that opt to stay on-air will be reassigned

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Then in 1993, Congress authorized the FCC to hold auctions to allocate spectrum licenses. Auctions offered great potential in terms of obtaining an efficient allocation of licenses and also capturing some of the value of the licenses to be returned to the U.S. taxpayers. However, the FCC was directed

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Trading on stock exchanges had been growing at a growing rate in the 1960s, 70s and 80s, which led Milgrom and coauthors (Bresnahan, Milgrom and Paul 1992) to ask whether the rapid increase of trading volume also brings rapid increase of the real output of stock exchanges. Traders in this model make

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and Barry Weingast (1990) presents a repeated game model that shows the role for a formal institution that serves as a repository of judgments about contract behavior to coordinate a multilateral reputation mechanism. Milgrom and his co-authors argued that this model sheds light on the development of

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Finally, Milgrom and Roberts (1986) bring the asymmetric information framework to bear in analyzing the issue of advertising and pricing. Traditionally, economists have thought of advertising as being either informative (as for example classified ads, which describe the characteristics of the product

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Returning to the issue of information asymmetry between incumbent and entrant, Milgrom and Roberts (1982b) consider the alternative case when the entrant is uncertain about the incumbent's costs. In this case, they show that the incumbent's low prices signal that its costs are low too, and so are the

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In the same paper, Milgrom introduced a novel "persuasion game", in which a salesperson has private information about a product, which he can, if he chooses, verifiably report to a potential buyer. (That is, the salesperson can, if he wishes, conceal his information, but he cannot misreport it if he

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periods and decide to punish or reward each other. This is now widely known as the "review strategy", and Milgrom's paper with D. Abreu and D. Pearce (Abreu, Milgrom and Pearce, 1991) was the first to show the efficiency of review strategy equilibrium in discounted repeated games. The review strategy

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Gillian K. Hadfield and Barry R. Weingast "What is Law? A Coordination Model of the Characteristics of Legal Order" Journal of Legal Analysis 4 (Winter 2012) 471-514; Gillian K. Hadfield and Barry R. Weingast "Law without the State: Legal Attributes and the Coordination of Decentralized Collective

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The behavioral critiques we have just discussed put these features of the rational choice approach to policy evaluation into question. Of course institutions affect preferences and some people are willing to exchange worse economic outcomes for a sense of control. Preferences may even be affected by

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The FCC needed an auction design suited to the sale of multiple licenses with potentially highly interdependent values. The FCC's goals included economic efficiency and revenue (although the legislation suggests an emphasis on efficiency over revenue) as well as operational simplicity and reasonable

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in this paper showed that if traders have the same prior beliefs and trading motives are purely speculative, then no trading should happen. This is because all traders correctly interpret the information reflected by the equilibrium prices and expect other people to trade rationally; as a result, an

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In their 1987 paper, Holmstrom and Milgrom introduced new techniques for studying multidimensional agency problems. The key insight in the Holmstrom-Milgrom paper is that simple linear incentive schemes can become optimal when the agent can monitor the evolution over time of the performance measures

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These conclusions do not mean that functional form assumptions are either useless or inconsequential for economic analysis. Functional form assumptions may be helpful for deriving explicit formulas for empirical estimation or simulations or simply to lend insight into the problem structure, and they

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Milgrom made a fundamental contribution to the theory of repeated games. When players' actions are hidden and noisy signals about their actions are observable (i.e., in the case of imperfect monitoring), there are two general ways to achieve efficiency. One way is to transfer future payoffs from one

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that vary from bidder to bidder. He analysed the bidding strategies in a number of well-known auction formats, demonstrating that a format will give the seller higher expected revenue when bidders learn more about each other's estimated values during bidding. Over time, societies have allocated ever

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Subsequent to receiving Congressional authorization, the FCC announced in March 2012 that Milgrom had been retained to lead a team of economists advising the FCC on the design of the incentive auctions. In September 2012, the FCC released Milgrom's preliminary report on the possible auction design.

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It seemed to provide bidders sufficient information and flexibility to pursue backup strategies to promote a reasonably efficient assignment of licenses, without so much complexity that the FCC could not successfully implement it and bidders could not understand it. Just having a good idea, though,

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to decide what counted as "cheating." In their model, merchants query the Law Merchant to determine whether a potential trading partner has cheated on prior contracts, triggering the application of punishment by other merchants. The incentive to punish in this model arises from the structure of the

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If Kreps, Milgrom, Roberts and Wilson (1982) effectively created a novel economic theory of reputation, Milgrom and Roberts (1982a), as well as Kreps and Wilson (1982), provided a first application to an outstanding issue of central importance in industrial organization theory and policy (predatory

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observed that when there is competition among informed, self-interested agents to persuade an uninformed party, all of the relevant information may be disclosed in equilibrium even if the uninformed party (e.g. the buyer) is not as sophisticated as was assumed in the analysis with a single informed

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Monotonic relationships, in which more of one quantity would imply more of another, are found pervasively in economic analysis. Milgrom pioneered in the development of new mathematical methods for understanding monotonic relationships in economics. His work on auctions with Robert Weber introduced

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His work on auction theory is probably his best-known. He has explored issues of design, bidding and outcomes for auctions with different rules. He designed auctions for multiple complementary items, with an eye towards practical applications such as frequency spectrum auctions. Professor Milgrom's

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profit by gathering information of the value of the firm and trading its stocks. However, information valuable for making a real decision on the firm is the value added rather than the value of the firm. Their analysis suggests that the increased trading activity increased the resources devoted to

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Milgrom's contribution to the understanding of legal institutions also includes one of the early express analyses of the functioning of adjudicatory institutions. In Milgrom and Roberts (1986b) the authors explore the role of strategic revelation in an adjudicatory setting. They show that the core

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Consider first the case of predatory pricing. For a long time, McGee's (1958) analysis, frequently associated with the Chicago school, provided the only coherent economic perspective regarding the main issues. McGee (1958) argued that the concept of predatory pricing lacks logical consistency. His

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Milgrom's path-breaking work has developed and popularized new tools for the analysis of asymmetric information and strategic interaction and, most significantly, has shown the usefulness of those tools for the analysis of applied problems," said Charles Manski, professor and chair of economics at

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In 2012, Auctionomics and Power Auctions were hired to design the FCC's first Incentive Auction, with the goal of creating a market for repurposing television broadcast spectrum to wireless broadband. The design team was led by Milgrom and includes Larry Ausubel, Kevin Leyton-Brown, Jon Levin and

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In 2009, Milgrom was responsible for the development of assignment auctions and exchanges. This was a mechanism that allowed for arbitrage possibilities and retained some of the flexibility of the simultaneous ascending bid auction but could be achieved instantaneously. The speed was an important

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When the auction began, Dr Milgrom's software tracked competitors' bids to estimate their budgets for the 1,132 licences on offer. Crucially, the software estimated the secret values bidders placed on specific licences and determined that certain big licences were being overvalued. It directed Dr

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In his teaching, Milgrom was always cognisant of what economic models could and could not do. He stressed the assumptions that made them useful in generating robust empirical predictions as well as the core assumptions upon which those predictions relied. This philosophy is perhaps exemplified in

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Milgrom's proposed design was adopted in large part by the commission. Called the simultaneous multiple round (SMR) auction, this design introduced several new features, mostly importantly an "activity rule" to ensure active bidding. Milgrom and Weber developed an activity rule to accompany their

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examined imperfections in labor markets. They evaluated the "Invisibility Hypothesis" which held that disadvantaged workers had difficult signalling their job skills to potential new employers because their existing employers denied them promotions that would improve visibility. Milgrom and Oster

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Milgrom and Roberts (1982a), as well as Kreps and Wilson (1982), provide a novel perspective on the issue. Methodologically, this perspective is based on the concept of reputation developed by Kreps, Milgrom, Roberts and Wilson (1982), where reputation is understood as the Bayesian posterior that

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In an influential paper, Milgrom and Roberts (1994) applied the framework of thinking about change of a system of complements to tackle some key issues in organizational economics. They noted that when organizations adapt by changing one element in a complementary system, it can often be the case

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to apply ideas from game theory and incentive theory to the study of organizations. Early on in this research, they focused on the importance of complementarities in organizational design. Activities in an organization are complementary, or synergistic, when there is a return to coordination. For

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will be linear in certain environments, Holmstrom and Milgrom then used linear contracts to explore in more detail what happens when agents allocate their efforts or attention across multiple tasks. Prior to 1991, models had generally considered effort on a single task. To reward performance on a

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is not enough. Good ideas need good advocates if they are to be adopted. No advocate was more persuasive than Paul Milgrom. He was so persuasive because of his vision, clarity and economy of expression, ability to understand and address FCC needs, integrity, and passion for getting things right.

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and Roberts (1992), Milgrom studied the influence costs that arise in multiunit firms. They demonstrate that managers of underperforming units have incentives to exaggerate the prospects of their unit in order to protect their jobs. If the unit were embedded in a firm whose other units were more

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In a series of papers, Milgrom studied the problem of lobbying and politicking, or "influence activities" that occur in large organizations. These papers considered models in which employees are affected by post-hiring decisions. When managers have discretion over these decisions, employees have

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Milgrom's research has often highlighted the restrictiveness (and often superfluity) of these assumptions in economic applications. For example, in the study of modern manufacturing (Milgrom and Roberts, 1990b), one would like to focus on the complementarity or substitutability across production

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models and search/matching models, have long had difficulty accounting for the observed volatility in labor market variables. In an influential paper, Shimer explained the problem as it appears in the standard search/matching model, an important macroeconomic model for which the Nobel prize was

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Proponents of the system, guided by a conception very like the standard one-dimensional incentive model, argue that these incentives will lead teachers to work harder at teaching and to take greater interest in their students' success. Opponents counter that the principal effect of the proposed

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According to FCC economist Evan Kwerel, who was given the task of developing the FCCís auction design, Milgrom's proposals, analysis, and research were hugely influential in the auction design. Milgrom and Wilson proposed a simultaneous ascending bid auction with discrete bidding rounds, which

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Appendix A in Milgrom and Roberts (1982a) proposes an alternative theory for equilibrium predatory pricing, that is, an alternative response to McGee's (1958) Chicago school criticism. In this appendix, Milgrom and Roberts examine an infinite horizon version of Selten's chain-store model (with

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Milgrom's role in creating the FCC design is noted in an account by the US National Science Foundation (America's Investment in the Future), which identifies this auction design as one of the main practical contributions of 20th century research in microeconomic theory. The same invention and

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Milgrom and Roberts first came on the ideas and applicability of complements when studying an enriched version of the classic news vendor problem of how to organize production that allowed both make to order after learning demand and make to stock (Milgrom and Roberts, 1988). The problem they

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if the player eventually chooses only nearly best-replies to their probabilistic forecast of the choices of other players, where the support of that probability distribution may include not only past plays but also strategies that the players might choose if they themselves were adaptive or

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I am delighted to have this world-class team of experts advising the Commission on this historic undertaking. Our plan is to ensure that incentive auctions serve as an effective market mechanism to unleash more spectrum for mobile broadband and help address the looming spectrum crunch. Our

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The impact and importance of the theory of supermodular games came from its breadth of application, including search, technology adoption, bank runs, arms races, pretrial negotiations, two-player Cournot competition, N-player Bertrand competition, and oil exploration, and the economics of

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with finitely many players, if the players' sets of types and actions are compact metric spaces, the players' payoffs are continuous functions of the types and actions, and the joint distribution of the players' types is absolutely continuous with respect to the product of their marginal

1305:, played a role in designing the simultaneous multiple round auction that was adopted and implemented by the FCC. Milgrom's auction theory research provided foundations that guided economists' thinking on auction design and ultimately the FCC's auction design choices. 824:

then it is consistent with adaptive learning. This gave a certain generality to those processes. They then showed how these processes related to the elimination of dominated strategies. This was shown to have implications for convergence in Cournot and Bertrand games.

1432:

In the run-up to an online auction in 2006 of radio-spectrum licences by America's Federal Communications Commission, Paul Milgrom, a consultant and Stanford University professor, customised his game-theory software to assist a consortium of bidders. The result was a

1094:

methods to describe the development of "modern manufacturing," characterized by frequent product redesigns and improvements, higher production quality, speedier communication and order processing, smaller batch sizes, and lower inventories. Subsequently, Milgrom and

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eventually chooses only strategies that are nearly best-replies to some probability distribution over the joint strategies of other players (with near zero probability being assigned to strategies that have not been played for a sufficiently long time). By contrast,

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in Economy, Finance and Management category "for his seminal contributions to an unusually wide range of fields of economics including auctions, market design, contracts and incentives, industrial economics, economics of organizations, finance, and game theory."

1049:. Milgrom and others have used this notion of favorableness and the associated "monotone likelihood ratio property" of information structures to derive a range of important results in information economics, from properties of the optimal incentive contract in a 1007:

reform would be that teachers would sacrifice such activities as promoting curiosity and creative thinking and refining students' oral and written communication skills in order to teach the narrowly defined basic skills that are tested on standardised exams.

515:

Weber recounted his collaboration with Milgrom. During what was supposed to be a brief meeting to ponder a problem faced by Weber, Milgrom had a key insight. Weber wrote, "And there, in a matter of a few minutes, was the heart of our first two joint papers."

1099:(1994), used similar methods to identify complementarities in incentive design. They argued that the use of high-intensity performance incentives would be complementary to placing relatively few restrictions on workers and decentralizing asset ownership. 1333:

In the words of Evan Kwerel, "In the end, the FCC chose an ascending bid mechanism, largely because we believed that providing bidders with more information would likely increase efficiency and, as shown by Milgrom and Weber (1982), mitigate the

1028:." The economists Bengt Holmstrom and Paul Milgrom describe the general problem of misaligned incentives in more formal terms – workers who are rewarded only for accomplishment of easily measurable tasks reduce the effort devoted to other tasks. 845:

The work of Milgrom and Shannon (1994) showed that comparative statics results could often be obtained through more relevant and intuitive ordinal conditions. Indeed, they show that their concept of quasi-supermodularity (a generalization of

1439:

Milgrom's clients to obtain a patchwork of smaller, less expensive licences instead. Two of his clients, Time Warner and Comcast, paid about a third less than their competitors for equivalent spectrum, saving almost $ 1.2 billion.

362:

School of Humanities and Sciences, a position he has held since 1987. He is a professor in the Stanford School of Engineering as well and a Senior Fellow at the Stanford Institute for Economic Research. Milgrom is an expert in

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and its applications in light of the developments in monotone comparative statics. Due to the influence of Milgrom and Shannon's paper and related research by Milgrom and others, these techniques, now often referred to as

739:. In Milgrom and Roberts (1991), they proposed two learning processes each with a degree of generality so as to not model learning but learning processes. They considered a sequence of plays over time which, for a player 838:

the concept of affiliation of random variables, to indicate systems of unknown quantities where learning that any one of them is higher than some given level would cause beliefs about others to be higher. His work with

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turns out to be useful when players receive private signals about each other's actions (the case of private monitoring), and the folk theorem for the private monitoring case is built on the idea of the review strategy.

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Holmstrom and Milgrom (1991) anticipated an important aspect of the debate in education on the issue of teacher pay and incentives. In considering incentive pay for teachers based on student test scores, they wrote:

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Milgrom made several fundamental contributions to game theory in the 1980s and 1990s on topics including the game-theoretic analysis of reputation formation, repeated games, supermodular games and learning in games.

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At the 2008 Nemmers Prize conference, Stephen Morris provided an explanation of Milgrom's contributions to the understanding of financial markets as well as of the impact that they have had on financial analysis.

527:. In 1987, Milgrom returned as an economics professor to his alma mater, Stanford University, where he is currently the Shirley and Leonard Ely Professor of Humanities and Sciences in the Department of Economics. 436:. Milgrom had a strong interest in math from a young age, which was fostered by his teachers. He attended the Ross summer math camp at Ohio State University in 1965, where he finished number one in his class. 617:

for his work involving auction design. In 2017, he won the CME Group-MSRI Prize in Innovative Quantitative Applications for his work in auction design. In 2020, he was appointed a Distinguished Fellow of the

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and Mark Satterthwaite that helped to bring game theory and information economics to bear on a wide range of problems in economics such as pricing, auctions, financial markets, and industrial organization.

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It would be better, these critics argue, to pay a fixed what without any incentive scheme than to base teachers' compensation only on the limited dimensions of student achievement that can be effectively

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Market design is a kind of economic engineering, utilizing laboratory research, game theory, algorithms, simulations, and more. Its challenges inspire us to rethink longstanding fundamentals of economic

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also advised regulators in the US, UK, Canada, Australia, Germany, Sweden and Mexico on spectrum auctions, Microsoft on search advertising auctions and Google on the auction at the basis of their IPO.

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Writing in 1994 on the comparative statics and theoretical modeling, Milgrom relates a theorem that would demonstrate when a result with a specific functional form may easily generalize, and notes:

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Gillian K. Hadfield and Barry R. Weingast "Law without the State: Legal Attributes and the Coordination of Decentralized Collective Punishment" Journal of Law and Courts 1 (Winter 2013) 1-23.

409:

Milgrom and his thesis advisor Wilson designed the auction protocol the FCC uses to determine which phone company gets what cellular frequencies. Milgrom also led the team that designed the

7709: 1087:, which led to their development and application of complementarity ideas in many spheres. The incorporation of these methods into economics, discussed below, has proved very influential. 1367:

Milgrom has taught a variety of courses in Economics. In the 1990s, he has developed a popular undergraduate course on The Modern Firm in Theory and Practice, based on his 1992 book with

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Ausubel, Lawrence M.; Cramton, Peter; Milgrom, Paul (2006). Cramton, Peter; Shoham, Yoav; Steinberg, Richard (eds.). "The Clock-Proxy Auction: A Practical Combinatorial Auction Design".

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Milgrom made early contributions to the growing literature applying game theoretic models to our understanding of the evolution of the legal institutions of the market economy. Milgrom,

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These insights have been built on to explore more generally the role of legal institutions in coordinating and incentivizing decentralized enforcement mechanisms like the multilateral

1024:

Too much pressure to improve students' test scores can reduce attention to other aspects of the curriculum and discourage cultivation of broader problem-solving skills, also known as "

7749: 866:(1994) extended this to comparative statics on equilibria, while Milgrom (1994) demonstrated its wider applicability in comparing optima. Milgrom and Roberts (1996) also generalized 5949: 1131:

In a series of three seminal papers, Milgrom and Roberts developed some of the central ideas regarding asymmetric information in the context of industrial organization. The work of

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example, a company that wants to make frequent changes in its production process will benefit from training workers in a flexible manner that allows them to adapt to these changes.

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as the 'publicity effect.') It provided a theoretical foundation for the intuition driving the major design choice by the FCC between an ascending bid and sealed bid auction.

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that performance will degrade. This will make change a hard sell within organizations. Milgrom and Roberts suggested that this is why businesses had been unable to replicate

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Milgrom, Paul; North, Douglass C.; Weingast, Barry R. (1990). "The role of institutions in the revival of trade: the law merchant, private judges, and the champagne fairs".

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complete information) and demonstrate the existence of an equilibrium where any attempted entry is met by predation — and thus entry does not take place in equilibrium.

1045:, if, for all prior beliefs about the variable of interest, the posterior belief conditional on x first-order stochastically dominates the posterior conditional on 842:

and Chris Shannon advanced the use of supermodularity as a property of individuals' preferences that can yield general monotonicity results in economic analysis.

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in 2008 "for contributions dramatically expanding the understanding of the role of information and incentives in a variety of settings, including auctions, the

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In 2011, the FCC hired Auctionomics to tackle one of the most complex auction problems ever, the incentive auction. FCC Chairman Julius Genachowski said,

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Milgrom and Stokey (1982) addressed an important question about why people trade securities and whether one can profit from speculation. The famous

3117: 6583: 6564: 6549: 6530: 5842: 4383: 1413: 719:

The theory of supermodular games is an important recent developments in economic theory. Key contributions to this theory include seminal work

372: 428:, Michigan, April 20, 1948, the second of four sons to Jewish parents Abraham Isaac Milgrom and Anne Lillian Finkelstein. His family moved to 593: 198: 735:

Milgrom and Roberts build on their work in supermodular games to understand the processes by which strategic agents reach equilibrium in a

4155:"Paul Milgrom wins the BBVA Foundation Frontiers of Knowledge Laureate for his contributions to auction theory and industrial organization" 410: 7719: 4181:"Paul Milgrom wins the BBVA Foundation Frontiers of Knowledge Award for his contributions to auction theory and industrial organization" 1443:

In 2007, Milgrom co-founded Auctionomics, with Silvia Console Battilana, to design auctions and advise bidders in different industries.

7739: 5806: 4252: 561: 5183:

Daughety, Andrew F.; Reinganum, Jennifer F. (2000). "On the Economics of Trials: Adversarial Process, Evidence and Equilibrium Bias".

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Ausubel, Lawrence M.; Milgrom, Paul (2006a). Cramton, P.; Shoham, Y.; Steinberg, R. (eds.). "The Lovely but Lonely Vickrey Auction".

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Greif, Avner; Milgrom, Paul; Weingast, Barry R. (1994). "Coordination, Commitment, and Enforcement: The Case of the Merchant Guild".

626: 208: 854:, is necessary and sufficient for comparative statics to obtain on arbitrary choice sets. Their theory extends earlier work in the 4752: 4278: 2429:

Holmstrom, Bengt; Milgrom, Paul (1991). "Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership and Job Design".

1037:

In Milgrom (1981), Milgrom introduced into economics a new notion of "favorableness" for information; namely, that one observation

413:

between 2016 and 2017, which was a two-sided auction to reallocate radio frequencies from TV broadcast to wireless broadband uses.

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Milgrom, Paul; Roberts, John (1994). "Complementarities and Fit: Strategy, Structure and Organizational Change in Manufacturing".

1233:

uninformed trader anticipates that he would incur a loss if he traded with an informed trader so would be better off not trading.

834:

inputs, without making assumptions on scale economies or divisibility (through a concavity condition on the production function).

5410:

Kwerel, Evan (2004), 'Foreword' in Paul Milgrom's Putting Auction Theory to Work, New York: Cambridge University Press, p.xviii.

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Froeb, Luke M.; Kobayashi, Bruce H. (1996). "Naïve, Biased, yet Bayesian: Can Juries Interpret Selectively Produced Evidence?".

4209: 5681: 2369:

Milgrom, Paul; Roberts, John (1990c). "Rationalizability, Learning and Equilibrium in Games With Strategic Complementarities".

573: 212: 193: 1268:(Hall and Milgrom, 2008), contributed to macroeconomics directly. Macroeconomic models, including real business cycle models, 7774: 6637: 5802: 4854: 4772: 4393: 3533:

Budish, E.; Che, Y.-K.; Kojima, F.; Milgrom, Paul (2013). "Designing Random Allocation Mechanisms: Theory and Applications".

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Milgrom, Paul; Qian, Yingi; Roberts, John (1991). "Complementarities, Momentum, and the Evolution of Modern Manufacturing".

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to hold the auction within a year, and at that time no suitable auction design existed, either in theory or in practice.

3930: 3162:

Ausubel, Lawrence M.; Milgrom, Paul (2006b). Cramton, P.; Shoham, Y.; Steinberg, R. (eds.). "Ascending Proxy Auctions".

7353: 6888: 6686: 5579: 4415: 3682: 2570: 2348:

Milgrom, Paul; Roberts, John (1990b). "The Economics of Modern Manufacturing: Technology, Strategy and Organization".

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Glosten, Larry; Milgrom, Paul (1985). "Bid, Ask and Transactions Prices in a Specialist Market with Insider Trading".

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Over the years, Milgrom has been active as an innovator and has been awarded four patents relating to auction design.

416:

In 2024, Milgrom's firm, Auctionomics, won a technical Emmy Award for their contributions to spectrum auction design.

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the Law Merchant, an institution of late medieval trade in Europe, whereby merchants looked to the judgments of the

50: 7744: 6793: 2262:

Fudenberg, Drew; Holmstrom, Bengt; Paul Milgrom (1990). "Short-term contracts and long-term agency relationships".

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Milgrom, Paul; Roberts, John (1987). "Informational Asymmetries, Strategic Behavior, and Industrial Organization".

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Grossman, Sanford J. (1981). "The Informational Role of Warranties and Private Disclosure about Product Quality".

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Milgrom, Paul; Roberts, John (1988). "An Economic Approach to Influence Activities and Organizational Responses".

1196:, an organization that has the power to punish its own members for failure to abide by a boycott announced by the 7734: 7262: 4029: 3812: 433: 5934: 4867: 2198:

Milgrom, Paul and John Roberts (1988). "Communication and Inventories as Substitutes in Organizing Production".

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attribute along with the potential to extend the auction design to consider bidding with non-price attributes.

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where he served from 1979 to 1983. Milgrom was part of a group of professors including future Nobel laureate

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Levin, Jonathan; Milgrom, Paul (2010). "Online Advertising: Heterogeneity and Conflation in Market Design".

7663: 7089: 6843: 6833: 6768: 3636: 1090:

In perhaps their most famous paper on organizations, (Milgrom and Roberts, 1990b) Milgrom and Roberts used

880: 335: 4842:

Francis Woolley also relates how the notation in that paper represented best practice in economic theory.

4318: 2592:; Paul Milgrom; Roberts, John (1992). "Organizational Prospects, Influence Costs, and Ownership Changes". 7779: 6883: 6863: 3763:"Jewish Economist with Detroit Roots Awarded 2020 Nobel Prize in Economic Sciences — Detroit Jewish News" 3737:"Jewish Economist with Detroit Roots Awarded 2020 Nobel Prize in Economic Sciences — Detroit Jewish News" 871: 693:

distributions. These basic assumptions are always satisfied if the sets of types and actions are finite.

403: 4564: 1424:

in bidding on FCC Auction 66 including a rarely successfully implemented "jump bid." In the words of the

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Milgrom, Paul (2010). "Ascending Prices and Package Bidding: A Theoretical and Experimental Analysis".

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Hall, Robert E.; Milgrom, Paul R. (2008). "The Limited Influence of Unemployment on the Wage Bargain".

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Milgrom, Paul; Roberts, John (1990a). "The Efficiency of Equity in Organizational Decision Processes".

2085: 1417: 1380: 637:

Paul Milgrom formulated a more general theory of auctions that not only allows common values, but also

544: 3958: 2580:

Bresnahan, Timothy F.; Milgrom, Paul; Paul, Jonathan (1992). "The Real Output of the Stock Exchange".

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Milgrom, Paul (1979b). "A Convergence Theorem for Competitive Bidding with Differential Information".

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on which his compensation will be based. In that paper, an agent continuously chooses the drift of an

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Fudenberg, D.; Levine, D.; Maskin E. (1994). "The Folk Theorem with Imperfect Public Information".

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Abreu, D.; Milgrom, Paul; Pearce, David (1991). "Information and Timing in Repeated Partnerships".

1930: 1879: 1717: 1689: 1653: 1513: 532: 7451: 5486: 5300: 4092: 3052: 1548:

Milgrom, Paul (1981b). "Rational Expectations, Information Acquisition, and Competitive Bidding".

560:, who had died three days after the Nobel prize announcement. In 2006, Milgrom was elected to the 7729: 7653: 7252: 7222: 6878: 6666: 6499: 5872: 2528:

Milgrom, Paul; Roberts, John (1991). "Adaptive and sophisticated learning in normal form games".

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Milgrom, Paul (2010). "Simplified mechanisms with an application to sponsored-search auctions".

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The single-crossing property as reformulated by Milgrom and Shannon was subsequently shown by

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With these definitions in place, Milgrom and Roberts showed that if a sequence converges to a

394:. He is the co-founder of several companies, the most recent of which, Auctionomics, provides 7137: 7122: 6696: 3882: 3111: 3024: 1212: 950: 847: 463:

in 1974. In 1975, Milgrom enrolled for graduate studies at Stanford University and earned an

183: 4279:"Paul Milgrom Awarded the 2017 CME Group-MSRI Prize in Innovative Quantitative Applications" 2891:

Milgrom, Paul (2000). "Putting Auction Theory to Work: The Simulteneous Ascending Auction".

944: 7699: 7471: 7456: 7343: 7338: 7242: 7227: 7192: 7157: 6756: 6701: 6623: 6419: 6236: 5763: 4256: 1577:

Milgrom, Paul (1981c). "Good News and Bad News: Representation Theorems and Applications".

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Shimer, Robert (2005). "The Cyclical Behavior of Equilibrium Unemployment and Vacancies".

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Milgrom, Paul (1994). "Comparing Optima: Do Simplifying Assumptions Affect Conclusions?".

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Milgrom, Paul (1994). "Comparing Optima: Do Simplifying Assumptions Affect Conclusions?".

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Upon receiving the Nemmers Prize in 2008, the official release highlighted the following:

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Milgrom, P. and Roberts, J. "Adaptive and sophisticated learning in normal form games,"

4344: 7607: 7466: 7297: 7277: 7127: 7006: 6911: 6838: 6783: 6363: 6045: 5393: 5345: 5235: 5200: 5165: 5138: 5130: 5076: 5068: 5023: 5015: 4935: 4927: 4872: 4825: 4733: 4698: 4487: 3637:"Nobel Prize in economics awarded to Paul Milgrom and Robert Wilson for auction theory" 3521: 3416: 3358:

Milgrom, Paul; Bruno Strulovici (2009). "Substitute goods, auctions, and equilibrium".

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Ausubel, Lawrence M.; Milgrom, Paul (2002). "Ascending Auctions with Package Bidding".

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at the Metropolitan Insurance Company and then at the Nelson and Warren consultancy in

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Topkis, D. (1968). Ordered Optimal Decisions. Ph.D. Dissertation, Stanford University.

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Milgrom, Paul; Weber, Robert (1982b). "A Theory of Auctions and Competitive Bidding".

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periods, and upon the release of information players "review" the signals in the last

42: 7592: 7561: 7516: 7411: 7282: 7237: 7212: 7142: 7016: 6946: 6936: 6828: 6778: 6726: 6475: 6471: 6443: 6431: 6196: 6156: 6148: 6049: 5752: 5337: 5270: 5080: 5027: 4980: 4976: 4939: 4829: 4817: 4812: 4795: 4768: 4737: 4678: 4659: 4654: 4637: 4545: 4531: 4442: 4389: 4364: 4360: 3874: 3525: 3516: 3499: 3455: 3189: 3172: 3148: 3097: 3037: 3020: 2965: 2879: 2787:

Milgrom, Paul; Roberts, John (1995). "The Economics of Modern Manufacturing: Reply".

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Shin Hyun Song (1998). "Adversarial and Inquisitorial Procedures in Arbitration".

4137:"Nemmers Awards in Economics, Mathematics Announced: Northwestern University News" 3695: 2985:

Milgrom, Paul; Segal, Ilya (2002). "Envelope Theorems for Arbitrary Choice Sets".

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In a further contribution in this area, Milgrom, together with Barry Weingast and

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Sugaya, T. (2013), "The Folk Theorem in Repeated Games with Private Monitoring,"

4319:"The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2020" 2397: 1269: 1136: 1096: 987: 975: 685: 557: 524: 504: 496: 264: 245: 7436: 5743: 4953:

Kreps, David M.; Wilson, Robert (1982). "Reputation and Imperfect Information".

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McGee, John S (1958). "Predatory Price Cutting: The Standard Oil (N. J.) Case".

3886: 2831:"Coalition-Proofness and Correlation with Arbitrary Communication Possibilities" 2579: 7511: 7501: 7491: 7426: 7416: 7406: 7391: 7187: 7167: 7152: 7147: 7107: 7074: 7059: 7054: 7044: 6853: 6603: 6572: 6542: 6511: 6391: 6323: 6319: 6288: 6256: 6224: 6172: 6124: 6108: 5997: 5791: 5635: 4694: 4343:

Kreps, David M; Milgrom, Paul; Roberts, John; Wilson, Robert (August 1, 1982).

2159:"Employment Contracts, Influence Activities, and Efficient Organization Design" 1802: 1618:"Limit Pricing and Entry Under Incomplete Information: An Equilibrium Analysis" 1617: 1298: 1176: 1140: 1132: 943:

His work comprises three broad theoretical and practical efforts in the field:

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In Combinatorial Auctions, Edited by Cramton, P., Shoham, Y., and Steinberg, R

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in economics. In related work, Milgrom and Ilya Segal (2002) reconsidered the

688:

on distributional strategies showed the general existence of equilibria for a

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Notation: A Beginner's Guide, Worthwhile Canadian Initiative, 17 April 2013.

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but also to give rise to a complete characterization of social preferences.

358:. He is the Shirley and Leonard Ely Professor of Humanities and Sciences at 7526: 7376: 6951: 6587: 6576: 6538: 6491: 6407: 6220: 6204: 6164: 6076: 5476:

Federal Communications Commission. March 27, 2012. Retrieved July 11, 2019.

4518:

Vives, Xavier (1990). "Nash Equilibrium with Strategic Complementarities".

4030:"Fellows of the Econometric Society 1950 to 2019 | The Econometric Society" 3532: 2961: 2847: 2830: 2720: 2700:

Holmstrom, Bengt; Milgrom, Paul (1994). "The Firm as an Incentive System".

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and was developed by Milgrom and Weber (1982). (Milgrom (2004) recasts the

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in 1992. In 1996, he gave the Nobel memorial lecture honoring the laureate

538: 500: 483:

Milgrom assumed a teaching position at the Kellogg School of Management at

391: 7770:

University of Michigan College of Literature, Science, and the Arts alumni

5640: 5333: 4428: 3713: 3556: 3490: 3264: 1898: 7643: 7446: 7441: 7421: 7217: 7202: 7011: 6981: 6916: 6906: 6736: 6671: 6647: 6483: 6467: 6395: 6280: 6212: 6116: 6080: 5698: 5182: 3224: 3207: 1189: 899: 887: 448: 364: 299: 291: 6615: 4482: 4437: 3412: 3272: 3233: 2588: 2323: 2284: 2029:"Aggregation and Linearity in the Provision of Intertemporal Incentives" 1907: 1745: 1119:

In 1992, Milgrom and Roberts published their textbook on organizations,

94: 7272: 6926: 6568: 6523: 6013: 5651: 5397: 5204: 5169: 5072: 5019: 4491: 3840: 3350: 3198: 3076: 3016: 2821: 2800: 2742: 2713: 2692: 2663: 2634: 2520: 2499: 2390: 2361: 2340: 2293: 2254: 2219: 2182: 2141: 2112: 2076: 2055: 2019: 1983: 1870: 1793: 1644: 1608: 1569: 1540: 1504: 902:

extended these results to consider economic problems with uncertainty.

520: 468: 380: 331: 5544: 5239: 5134: 4931: 3208:"What the Seller Won't Tell You: Persuasion and Disclosure in Markets" 2922: 2671:

Milgrom, Paul; Shannon, Chris (1994). "Monotone Comparative Statics".

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Market Design: A Linear Programming Approach to Auctions and Matching

3624:(Press release). Royal Swedish Academy of Sciences. October 12, 2020. 2506: 993:

Having demonstrated that the optimal incentive contract in a dynamic

355: 230: 4473: 2684: 2491: 2382: 2211: 2104: 2047: 1829:

Engelbrecht-Wiggans, R.; Milgrom, Paul R.; Weber, Robert J. (1983).

1785: 1636: 1600: 1561: 1532: 1496: 53:. Statements consisting only of original research should be removed. 7612: 7112: 5126: 5064: 5011: 4923: 4729: 2914: 2808:

Milgrom, Paul; Roberts, John (1996a). "The LeChatelier Principle".

2734: 2626: 2467: 2174: 2133: 2086:"Job Discrimination, Market Forces and the Invisibility Hypothesis" 1975: 1801:

Kreps, David; Milgrom, Paul; Roberts, John; Wilson, Robert (1982).

395: 125: 5657: 4345:"Rational cooperation in the finitely repeated prisoners' dilemma" 3288:

Day, R.; Milgrom, Paul (2008). "Core-selecting package auctions".

3161: 3124: 1857:

Milgrom, Paul (1984). "Axelrod's "The Evolution of Cooperation"".

1803:"Rational Cooperation in the Finitely‑Repeated Prisoners' Dilemma" 1651: 7333: 7323: 7001: 5217: 4626:

Veinott, A. F. (1989). Lattice programming. Unpublished lectures.

4411:"Distributional Strategies for Games with Incomplete Information" 2937: 1880:"Distributional Strategies for Games with Incomplete Information" 1421: 425: 399: 121: 4459: 4078:

Procuring Universal Service: Putting Auction Theory to Work, in

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Farmer, Amy; Pecorino, Paul (2000). "Does jury bias matter?".

3050: 2197: 7102: 4998:

Nelson, Phillip (1970). "Information and Consumer Behavior".

4952: 4206:"BBVA Foundation Frontiers of Knowledge Award Citation, 2012" 3357: 2699: 2650:

Milgrom, Paul; Roberts, John (1994). "Comparing Equilibria".

2428: 2026: 1316:

Describing the Milgrom-Wilson auction design, Kwerel states:

1197: 1193: 472: 7710:

Center for Advanced Study in the Behavioral Sciences fellows

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literature (Topkis, 1968; Veinott, 1989) which already uses

519:

From 1982 to 1987, Milgrom was a professor of economics and

432:, and Milgrom attended the Dewey Elementary School and then 379:, "for improvements to auction theory and inventions of new 5474:

Leading Auction Experts to Advise FCC on Incentive Auctions

5318:"The Limited Influence of Unemployment on the Wage Bargain" 5094:

Punishment" Journal of Law and Courts 1 (Winter 2013) 1-23.

3327:

Milgrom, Paul (2009). "Assignment Messages and Exchanges".

2828: 2807: 2670: 2368: 2347: 2300: 1998: 1954: 1915: 1761: 1715: 964: 464: 444: 4591:

See also Gans, J.S. "Best Replies and Adaptive Learning,"

2786: 2757: 2649: 2556: 2527: 2119: 2083: 2062: 1877: 1687: 1615: 625:

In October 2020, Milgrom was the co-recipient of the 2020

7750:

Members of the United States National Academy of Sciences

5624: 5563:"Milgrom, P. (2009), "Assignment Messages and Exchange."" 5457:"Broadcast Incentive Auction and Post-Auction Transition" 5252: 4342: 3641: 1170: 773:) is a pure strategy. Given this, an observed sequence, { 16:

Economist and winner of the 2020 Nobel Prize in Economics

2984: 1379:

this reflect on the assumption of rational choice (with

4759:, Cambridge: Cambridge University Press, pp. 1–8, 4409:

Milgrom, Paul R.; Weber, Robert J. (November 1, 1985).

3984:"Bob Weber's Memories: Working with Paul Milgrom, 2013" 5041:

Nelson, Phillip (1974). "Advertising as Information".

609:

In 2013, Milgrom was elected as Vice President of the

723:, Vives (1990), and the Milgrom and Roberts (1990c). 7715:

Fellows of the American Academy of Arts and Sciences

5112: 4115:"2008 Erwin Plein Nemmers Economics Prize Recipient" 3287: 7765:

Stanford University Department of Economics faculty

4635: 3867:

The Structure of Information in Competitive Bidding

3858: 3613: 3611: 1514:"An Axiomatic Characterization of Common Knowledge" 1475:

The Structure of Information in Competitive Bidding

1338:." The result alluded to by Kwerel is known as the 883:, are widely known and used in economic modelling. 265:

The structure of information in competitive bidding

5316:Hall, Robert E; Milgrom, Paul R (August 1, 2008). 4796:"Critical Issues in the Practice of Market Design" 4638:"Majority Voting With Single-Crossing Preferences" 3500:"Critical Issues in the Practice of Market Design" 2558: 2001:"Relying on the Information of Interested Parties" 1957:"Price and Advertising Signals of Product Quality" 1718:"The Value of Information in a Sealed Bid Auction" 890:and Michael Smart not only to resolve Condorcet's 1831:"Competitive bidding and proprietary information" 7691: 4679:"Monotone Comparative Statics under Uncertainty" 3608: 371:and pricing strategies. He is the winner of the 5040: 4997: 4381: 4232:"Officers of the American Economic Association" 1244:, without improving real investment decisions. 451:. He worked as an actuary for several years in 5696: 5365: 5155: 2594:Journal of Economics & Management Strategy 1576: 1547: 1511: 1482: 1472: 1074:In the late 1980s, Milgrom began working with 862:but focuses on cardinal concepts. Milgrom and 373:2020 Nobel Memorial Prize in Economic Sciences 6631: 5950: 5682: 5220:Journal of Law, Economics, & Organization 5185:Journal of Law, Economics, & Organization 4909: 4517: 3683:Incentive Auction Rules Option and Discussion 3497: 3427: 3388: 3326: 3205: 3170: 3031: 2890: 2855: 2612: 2431:Journal of Law, Economics, & Organization 2226: 2156: 1856: 1654:"Predation, Reputation, and Entry Deterrence" 1652:Milgrom, Paul; Roberts, John Roberts (1982). 1281: 1218: 5970:Sveriges Riksbank Prize in Economic Sciences 5498:Bulow, J., J. Levin and P. Milgrom (2009), " 4408: 4055:"Paul Milgrom's Profile | Stanford Profiles" 3116:: CS1 maint: multiple names: authors list ( 1264:Two decades later, Milgrom, in a paper with 727:organizations (Milgrom and Roberts, 1990b). 679: 594:BBVA Foundation Frontiers of Knowledge Award 199:BBVA Foundation Frontiers of Knowledge Award 5315: 4565:"Standord University - Super Modular Games" 1069: 1041:is more favorable than another observation 600:The jury citation for the BBVA Award wrote: 419: 6638: 6624: 5957: 5943: 5689: 5675: 5644: 4676: 4385:A Long-run Collaboration on Long-run Games 4382:Fudenberg, Drew; Levine, David K. (2009). 2582:Output Measurement in the Services Sectors 1466: 1126: 93: 6645: 5379: 5255:International Review of Law and Economics 5054: 4966: 4811: 4653: 4539: 4481: 4436: 3546: 3515: 3480: 3441: 3402: 3391:American Economic Journal: Microeconomics 3371: 3340: 3329:American Economic Journal: Microeconomics 3301: 3254: 3223: 3188: 3134: 3051:Hatfield, John W.; Milgrom, Paul (2005). 2998: 2951: 2940:The B.E. Journal of Theoretical Economics 2904: 2873: 2846: 2481: 2442: 2411: 2322: 2283: 2244: 1929: 1906: 1775: 1744: 1690:"Information, Trade and Common Knowledge" 1590: 1349: 627:Nobel Memorial Prize in Economic Sciences 209:Nobel Memorial Prize in Economic Sciences 69:Learn how and when to remove this message 4255:. The Golden Goose Award. Archived from 3760: 3734: 2027:Holmstrom, Bengt; Milgrom, Paul (1987). 1032: 965:Organizational and information economics 530:Milgrom held editorial positions at the 4793: 4750: 4715: 3931:"UCLA - Putting Auction Theory to Work" 3864: 3145:10.7551/mitpress/9780262033428.003.0002 3094:10.7551/mitpress/9780262033428.001.0001 2858:"Game theory and the spectrum auctions" 655: 7692: 3661: 3659: 2829:Milgrom, Paul; Roberts, John (1996b). 2561:Economics, Organization and Management 1999:Milgrom, Paul; Roberts, John (1986b). 1955:Milgrom, Paul; Roberts, John (1986a). 1716:Milgrom, Paul; Weber, Robert (1982a). 1297:Milgrom, together with Robert Wilson, 1171:Law, institutions and economic history 1121:Economics, Organization and Management 828: 810:consistent with sophisticated learning 574:Erwin Plein Nemmers Prize in Economics 213:Technology and Engineering Emmy Awards 194:Erwin Plein Nemmers Prize in Economics 6619: 5938: 5670: 5361: 5359: 5311: 5309: 4887:"Roberts' Nemmers Presentation, 2008" 4562: 4080:Le Prix Nobel: The Nobel Prizes, 1996 3900: 3898: 3896: 3835: 3833: 3678: 3676: 3634: 3619:"The Prize in Economic Sciences 2020" 2557:Milgrom, Paul; Roberts, John (1992). 2084:Milgrom, Paul; Oster, Sharon (1987). 1878:Milgrom, Paul; Weber, Robert (1985). 1688:Milgrom, Paul; Stokey, Nancy (1982). 1616:Milgrom, Paul; Roberts, John (1982). 1223: 714: 554:American Academy of Arts and Sciences 354:(born April 20, 1948) is an American 4855:Holmstrom Nemmers Presentation, 2008 3963:Stanford Graduate School of Business 3910:Stanford Graduate School of Business 3761:Schwartz, Danny (October 12, 2020). 3735:Schwartz, Danny (October 12, 2020). 3595:Stanford Graduate School of Business 3290:International Journal of Game Theory 2233:The Journal of Economic Perspectives 1371:. In the early 2000s, together with 730: 567: 18: 5287:Yeon-Koo Che and Sergei Severinov " 5232:10.1093/oxfordjournals.jleo.a023361 3656: 3635:Riley, Charles (October 12, 2020). 2760:Journal of Accounting and Economics 13: 7720:Fellows of the Econometric Society 6687:First-player and second-player win 5356: 5306: 4416:Mathematics of Operations Research 4082:, Nobel Foundation, 1997, 382-392. 3893: 3830: 3673: 2422:10.1111/j.1468-0343.1990.tb00020.x 1887:Mathematics of Operations Research 660:In an influential 1982 paper with 478: 14: 7791: 7740:Jewish American social scientists 5616: 5587:Federal Communications Commission 5500:Winning Play in Spectrum Auctions 5461:Federal Communications Commission 5301:Morris Nemmers Presentation, 2008 4595:, Vol.30, No.3, 1995, pp.221-234. 4563:Levin, Jonathan (April 1, 2006). 4520:Journal of Mathematical Economics 4005:"All Publications | Paul Milgrom" 3696:"75th Award Recipients TechEmmys" 2200:Scandinavian Journal of Economics 1838:Journal of Mathematical Economics 1725:Journal of Mathematical Economics 1288:Federal Communications Commission 958:simplifying participants' message 788:consistent with adaptive learning 756:)} where for each possible time, 696: 459:. Milgrom became a Fellow of the 7705:21st-century American economists 6794:Coalition-proof Nash equilibrium 5485:Levin, Jonathan; Milgrom, Paul " 4813:10.1111/j.1465-7295.2010.00357.x 3517:10.1111/j.1465-7295.2010.00357.x 3212:Journal of Economic Perspectives 3190:10.1111/j.1468-0262.2007.00778.x 3173:"Package Auctions and Exchanges" 2606:10.1111/j.1430-9134.1992.00009.x 2229:"Auctions and Bidding: A Primer" 1251: 969: 919: 23: 6046:Leonid Vitaliyevich Kantorovich 5601: 5572: 5555: 5537: 5509: 5492: 5479: 5467: 5449: 5440: 5431: 5422: 5413: 5404: 5294: 5281: 5246: 5211: 5176: 5149: 5106: 5097: 5087: 5034: 4991: 4946: 4903: 4879: 4868:What Makes Teachers Productive? 4860: 4848: 4836: 4787: 4744: 4709: 4670: 4629: 4620: 4611: 4608:, Vol.3, No.3, 1991, pp.82-100. 4598: 4585: 4556: 4511: 4498: 4453: 4402: 4375: 4336: 4311: 4301:"American Economic Association" 4293: 4271: 4245: 4224: 4198: 4173: 4147: 4129: 4107: 4085: 4072: 4047: 4022: 3997: 3976: 3951: 3923: 3805: 3780: 2453:10.1093/jleo/7.special_issue.24 1016:This work was mentioned in the 6804:Evolutionarily stable strategy 5608:Patents Issued to Paul Milgrom 5446:Kwerel, op.cit., 2004, p.xvii. 4683:Quarterly Journal of Economics 4636:Gans, J.S.; Smart, M. (1996). 4095:. National Academy of Sciences 3813:"Paul R. Milgrom Biographical" 3754: 3728: 3702: 3688: 3628: 3583: 3571:List of Jewish Nobel laureates 3036:. Cambridge University Press. 3034:Putting Auction Theory to Work 2093:Quarterly Journal of Economics 1918:Journal of Financial Economics 646: 580:, and oligopolistic markets." 1: 6732:Simultaneous action selection 5487:Introduction to Choice Theory 5428:Kwerel, op.cit., 2004, p.xxi. 5419:Kwerel, 2004, op.cit., p.xix. 5267:10.1016/s0144-8188(00)00033-8 4751:Bichler, Martin, ed. (2017), 3865:Milgrom, Paul Robert (1979). 3576: 2875:10.1016/S0014-2921(97)00146-3 2122:American Journal of Sociology 2008:The RAND Journal of Economics 1859:The RAND Journal of Economics 620:American Economic Association 611:American Economic Association 7775:Nobel laureates in Economics 7664:List of games in game theory 6844:Quantal response equilibrium 6834:Perfect Bayesian equilibrium 6769:Bayes correlated equilibrium 5437:Kwerel, op.cit., 2004, p.xx. 5368:The American Economic Review 5115:Journal of Law and Economics 5043:Journal of Political Economy 5000:Journal of Political Economy 4977:10.1016/0022-0531(82)90030-8 4912:Journal of Law and Economics 4718:Journal of Political Economy 4655:10.1016/0047-2727(95)01503-5 4593:Mathematical Social Sciences 4532:10.1016/0304-4068(90)90005-t 4361:10.1016/0022-0531(82)90029-1 3792:www.jewishvirtuallibrary.org 3243:The American Economic Review 3057:The American Economic Review 2893:Journal of Political Economy 2810:The American Economic Review 2789:The American Economic Review 2772:10.1016/0165-4101(94)00382-f 2723:Journal of Political Economy 2702:The American Economic Review 2652:The American Economic Review 2615:Journal of Political Economy 2542:10.1016/0899-8256(91)90006-Z 2509:The American Economic Review 2315:10.1016/0022-0531(90)90048-O 2303:The American Economic Review 2276:10.1016/0022-0531(90)90048-O 2163:Journal of Political Economy 2065:The American Economic Review 1964:Journal of Political Economy 1940:10.1016/0304-405X(85)90044-3 1850:10.1016/0304-4068(83)90034-4 1822:10.1016/0022-0531(82)90029-1 1737:10.1016/0304-4068(82)90008-8 1709:10.1016/0022-0531(82)90046-1 1673:10.1016/0022-0531(82)90031-X 881:monotone comparative statics 562:National Academy of Sciences 548:. He became a Fellow of the 398:and services for commercial 386:He is the co-creator of the 7: 7133:Optional prisoner's dilemma 6864:Self-confirming equilibrium 4642:Journal of Public Economics 4606:Games and Economic Behavior 4009:milgrom.people.stanford.edu 3564: 3430:Games and Economic Behavior 2835:Games and Economic Behavior 2530:Games and Economic Behavior 1403: 1362: 439:Milgrom graduated from the 411:broadcast incentive auction 49:the claims made and adding 10: 7796: 7760:Stanford University alumni 7598:Principal variation search 7314:Aumann's agreement theorem 6977:Strategy-stealing argument 6889:Trembling hand equilibrium 6819:Markov perfect equilibrium 6814:Mertens-stable equilibrium 6038:Friedrich August von Hayek 5654:on EconBiz Author Profiles 5545:"Silvia Console Battilana" 4955:Journal of Economic Theory 4695:10.1162/003355302753399481 4349:Journal of Economic Theory 4161:(in Spanish). June 2, 2017 4034:www.econometricsociety.org 3360:Journal of Economic Theory 2264:Journal of Economic Theory 1810:Journal of Economic Theory 1697:Journal of Economic Theory 1661:Journal of Economic Theory 1477:. New York: Garland Press. 1282:FCC spectrum auction, 1993 1219:Finance and macroeconomics 923: 684:Milgrom's 1985 paper with 545:Journal of Economic Theory 7634:Combinatorial game theory 7621: 7580: 7362: 7306: 7293:Princess and monster game 7088: 6990: 6897: 6849:Quasi-perfect equilibrium 6774:Bayesian Nash equilibrium 6755: 6654: 6436:Christopher A. Pissarides 6310: 6059: 5976: 5867: 5837: 5801: 5770: 5751: 5731: 5706: 5517:"Game theory in practice" 5289:Lawyer-advised Disclosure 5158:RAND Journal of Economics 4765:10.1017/9781316779873.001 3452:10.1016/j.geb.2008.12.003 3382:10.1016/j.jet.2008.05.002 3312:10.1007/s00182-007-0100-7 3164:In Combinatorial Auctions 3127:In Combinatorial Auctions 3053:"Matching with Contracts" 1579:Bell Journal of Economics 1276: 1012:. (Emphasis in original). 680:Distributional strategies 424:Paul Milgrom was born in 345: 341: 330: 325: 321: 317: 313: 287: 275: 257: 236: 226: 219: 189: 179: 161: 133: 104: 92: 85: 7649:Evolutionary game theory 7382:Antoine Augustin Cournot 7268:Guess 2/3 of the average 7065:Strictly determined game 6859:Satisfaction equilibrium 6677:Escalation of commitment 5634:publications indexed by 5390:10.1257/0002828053828572 5322:American Economic Review 5303:Retrieved July 10, 2019. 4857:Retrieved July 11, 2019. 3535:American Economic Review 3469:American Economic Review 3069:10.1257/0002828054825466 2862:European Economic Review 2350:American Economic Review 1070:Organizational economics 872:Le Chatelier's Principle 852:single-crossing property 533:American Economic Review 420:Early life and education 7745:Mathematical economists 7654:Glossary of game theory 7253:Stackelberg competition 6879:Strong Nash equilibrium 3009:10.1111/1468-0262.00296 1512:Milgrom, Paul (1981a). 1473:Milgrom, Paul (1979a). 1467:Publications (selected) 1127:Industrial organization 1053:, to the notion of the 1051:principal-agent problem 995:principal-agent problem 974:Milgrom, together with 894:in majority voting and 485:Northwestern University 360:the Stanford University 336:IDEAS / RePEc 241:Northwestern University 7735:Information economists 7679:Tragedy of the commons 7659:List of game theorists 7639:Confrontation analysis 7349:Sprague–Grundy theorem 6869:Sequential equilibrium 6789:Correlated equilibrium 5873:Nobel Prize recipients 5803:Physiology or Medicine 5716:Emmanuelle Charpentier 4794:Milgrom, Paul (2011). 3498:Milgrom, Paul (2011). 3206:Milgrom, Paul (2008). 3171:Milgrom, Paul (2007). 3032:Milgrom, Paul (2004). 2962:10.2202/1534-5963.1019 2856:Milgrom, Paul (1998). 2848:10.1006/game.1996.0096 2400:Economics and Politics 2227:Milgrom, Paul (1989). 2157:Milgrom, Paul (1988). 1441: 1435: 1401: 1395: 1389: 1350:FCC incentive auctions 1323: 1256:In 1987, Milgrom with 1030: 1014: 941: 917: 912: 822:correlated equilibrium 644: 607: 590: 441:University of Michigan 138:University of Michigan 7452:Jean-François Mertens 6157:James M. Buchanan Jr. 5334:10.1257/aer.98.4.1653 5197:10.1093/jleo/16.2.365 4899:on February 20, 2014. 4876:, September 19, 2011. 4429:10.1287/moor.10.4.619 4059:profiles.stanford.edu 3557:10.1257/aer.103.2.585 3491:10.1257/aer.100.2.603 3265:10.1257/aer.98.4.1653 1899:10.1287/moor.10.4.619 1436: 1430: 1396: 1390: 1385: 1318: 1033:Information economics 1022: 1004: 936: 913: 907: 848:supermodular function 635: 602: 585: 572:Milgrom received the 475:in business in 1979. 7725:Financial economists 7581:Search optimizations 7457:Jennifer Tour Chayes 7344:Revelation principle 7339:Purification theorem 7278:Nash bargaining game 7243:Bertrand competition 7228:El Farol Bar problem 7193:Electronic mail game 7158:Lewis signaling game 6702:Hierarchy of beliefs 6420:Oliver E. Williamson 6050:Tjalling C. Koopmans 5764:World Food Programme 4388:. World Scientific. 4141:www.northwestern.edu 3698:. February 22, 2024. 3225:10.1257/jep.22.2.115 3129:. MIT press: 17–40. 1479:(Ph.D. Dissertation) 1412:In 2006, along with 1026:teaching to the test 896:social choice theory 656:Reputation formation 613:. In 2014, he won a 461:Society of Actuaries 434:Oak Park High School 7629:Bounded rationality 7248:Cournot competition 7198:Rock paper scissors 7173:Battle of the sexes 7163:Volunteer's dilemma 7035:Perfect information 6962:Dominant strategies 6799:Epsilon-equilibrium 6682:Extensive-form game 6448:Christopher A. Sims 6376:Thomas C. Schelling 6348:Robert F. Engle III 6249:Robert E. Lucas Jr. 6097:Theodore W. Schultz 5580:"FCC Press Release" 5525:. September 3, 2011 4677:Athey S.C. (2002). 4572:Stanford University 4259:on October 12, 2020 4186:. February 13, 2012 3871:Stanford University 3845:Stanford University 3685:September 12, 2012. 3413:10.1257/mic.2.3.160 1092:comparative statics 1057:in auction theory. 856:Operations Research 829:Comparative statics 550:Econometric Society 352:Paul Robert Milgrom 251:Stanford University 147:Stanford University 7780:American actuaries 7608:Paranoid algorithm 7588:Alpha–beta pruning 7467:John Maynard Smith 7298:Rendezvous problem 7138:Traveler's dilemma 7128:Gift-exchange game 7123:Prisoner's dilemma 7040:Large Poisson game 7007:Bargaining problem 6912:Backward induction 6884:Subgame perfection 6839:Proper equilibrium 6364:Edward C. Prescott 6352:Clive W.J. Granger 6328:Joseph E. Stiglitz 6301:Daniel L. McFadden 6189:Harry M. Markowitz 5643:on Nobelprize.org 5463:. January 8, 2016. 4873:The New York Times 4541:10338.dmlcz/141568 3716:on August 13, 2017 3710:"Curriculum Vitae" 3351:10.1257/mic.1.2.95 1420:, Milgrom advised 1224:Securities markets 930:Milgrom describes 870:'s application of 715:Supermodular games 674:Kreps et.al., 1982 615:Golden Goose Award 578:theory of the firm 430:Oak Park, Michigan 204:Golden Goose Award 34:possibly contains 7687: 7686: 7593:Aspiration window 7562:Suzanne Scotchmer 7517:Oskar Morgenstern 7412:Donald B. Gillies 7354:Zermelo's theorem 7283:Induction puzzles 7238:Fair cake-cutting 7213:Public goods game 7143:Coordination game 7017:Intransitive game 6947:Forward induction 6829:Pareto efficiency 6809:Gibbs equilibrium 6779:Berge equilibrium 6727:Simultaneous game 6613: 6612: 6512:Richard H. Thaler 6476:Robert J. Shiller 6472:Lars Peter Hansen 6444:Thomas J. Sargent 6432:Dale T. Mortensen 6324:A. Michael Spence 6320:George A. Akerlof 6289:Robert A. Mundell 6257:James A. Mirrlees 6225:Douglass C. North 6197:William F. Sharpe 6149:Franco Modigliani 6125:George J. Stigler 6109:Lawrence R. Klein 5998:Paul A. Samuelson 5932: 5931: 5839:Economic Sciences 4774:978-1-107-17318-7 4395:978-981-281-846-1 4159:Premios Fronteras 4093:"Paul R. Milgrom" 3906:"Paul R. Milgrom" 3591:"Paul R. Milgrom" 3103:978-0-2620-3342-8 3043:978-0-521-53672-1 2565:. Prentice Hall. 2246:10.1257/jep.3.3.3 1344:linkage principle 1340:Linkage principle 1205:reputation system 1139:, and especially 850:) along with the 731:Learning in games 568:Awards and honors 552:in 1984, and the 349: 348: 288:Doctoral students 221:Scientific career 79: 78: 71: 36:original research 7787: 7674:Topological game 7669:No-win situation 7567:Thomas Schelling 7547:Robert B. Wilson 7507:Merrill M. Flood 7477:John von Neumann 7387:Ariel Rubinstein 7372:Albert W. Tucker 7223:War of attrition 7183:Matching pennies 6824:Nash equilibrium 6747:Mechanism design 6712:Normal-form game 6667:Cooperative game 6640: 6633: 6626: 6617: 6616: 6606: 6598: 6596:Philip H. Dybvig 6579: 6560: 6558:Robert B. Wilson 6545: 6535:Abhijit Banerjee 6526: 6520:William Nordhaus 6514: 6506: 6494: 6486: 6478: 6462: 6460:Lloyd S. Shapley 6450: 6438: 6428:Peter A. Diamond 6422: 6410: 6402: 6400:Roger B. Myerson 6386: 6384:Edmund S. Phelps 6378: 6372:Robert J. Aumann 6366: 6354: 6342: 6330: 6303: 6297:James J. Heckman 6291: 6283: 6275: 6273:Myron S. Scholes 6269:Robert C. Merton 6263: 6251: 6243: 6237:John F. Nash Jr. 6233:John C. Harsanyi 6227: 6215: 6207: 6199: 6193:Merton H. Miller 6183: 6175: 6167: 6159: 6151: 6143: 6135: 6127: 6119: 6111: 6103: 6101:Sir Arthur Lewis 6091: 6089:Herbert A. Simon 6083: 6071: 6052: 6040: 6028: 6026:Wassily Leontief 6020: 6018:Kenneth J. Arrow 6008: 6000: 5992: 5959: 5952: 5945: 5936: 5935: 5875: 5858:Robert B. Wilson 5824:(United Kingdom) 5822:Michael Houghton 5782:(United Kingdom) 5691: 5684: 5677: 5668: 5667: 5663:publication list 5648: 5628: 5627: 5625:Official website 5610: 5605: 5599: 5598: 5596: 5594: 5589:. March 27, 2012 5584: 5576: 5570: 5569: 5567: 5559: 5553: 5552: 5549:web.stanford.edu 5541: 5535: 5534: 5532: 5530: 5513: 5507: 5496: 5490: 5483: 5477: 5471: 5465: 5464: 5453: 5447: 5444: 5438: 5435: 5429: 5426: 5420: 5417: 5411: 5408: 5402: 5401: 5383: 5363: 5354: 5353: 5328:(4): 1653–1674. 5313: 5304: 5298: 5292: 5285: 5279: 5278: 5250: 5244: 5243: 5215: 5209: 5208: 5180: 5174: 5173: 5153: 5147: 5146: 5110: 5104: 5101: 5095: 5091: 5085: 5084: 5058: 5038: 5032: 5031: 4995: 4989: 4988: 4970: 4950: 4944: 4943: 4907: 4901: 4900: 4898: 4892:. Archived from 4891: 4883: 4877: 4864: 4858: 4852: 4846: 4840: 4834: 4833: 4815: 4800:Economic Inquiry 4791: 4785: 4784: 4783: 4781: 4748: 4742: 4741: 4713: 4707: 4706: 4674: 4668: 4667: 4657: 4633: 4627: 4624: 4618: 4615: 4609: 4602: 4596: 4589: 4583: 4582: 4580: 4578: 4569: 4560: 4554: 4553: 4543: 4515: 4509: 4502: 4496: 4495: 4485: 4457: 4451: 4450: 4440: 4406: 4400: 4399: 4379: 4373: 4372: 4340: 4334: 4333: 4331: 4329: 4315: 4309: 4308: 4297: 4291: 4290: 4288: 4286: 4275: 4269: 4268: 4266: 4264: 4253:"Auction Design" 4249: 4243: 4242: 4240: 4238: 4228: 4222: 4221: 4219: 4217: 4212:on June 21, 2013 4208:. Archived from 4202: 4196: 4195: 4193: 4191: 4185: 4177: 4171: 4170: 4168: 4166: 4151: 4145: 4144: 4133: 4127: 4126: 4124: 4122: 4111: 4105: 4104: 4102: 4100: 4089: 4083: 4076: 4070: 4069: 4067: 4065: 4051: 4045: 4044: 4042: 4040: 4026: 4020: 4019: 4017: 4015: 4001: 3995: 3994: 3992: 3990: 3980: 3974: 3973: 3971: 3969: 3955: 3949: 3948: 3946: 3944: 3935: 3927: 3921: 3920: 3918: 3916: 3902: 3891: 3890: 3869:(Ph.D. thesis). 3862: 3856: 3855: 3853: 3851: 3837: 3828: 3827: 3825: 3823: 3809: 3803: 3802: 3800: 3798: 3784: 3778: 3777: 3775: 3773: 3758: 3752: 3751: 3749: 3747: 3732: 3726: 3725: 3723: 3721: 3712:. Archived from 3706: 3700: 3699: 3692: 3686: 3680: 3671: 3670: 3663: 3654: 3653: 3651: 3649: 3632: 3626: 3625: 3623: 3615: 3606: 3605: 3603: 3601: 3587: 3560: 3550: 3529: 3519: 3504:Economic Inquiry 3494: 3484: 3463: 3445: 3424: 3406: 3385: 3375: 3354: 3344: 3323: 3305: 3296:(3–4): 393–407. 3284: 3258: 3249:(4): 1653–1674. 3237: 3227: 3202: 3192: 3167: 3158: 3138: 3121: 3115: 3107: 3080: 3047: 3028: 3002: 2981: 2955: 2934: 2908: 2887: 2877: 2868:(3–5): 771–778. 2852: 2850: 2825: 2804: 2783: 2766:(2–3): 179–208. 2754: 2717: 2696: 2667: 2646: 2609: 2585: 2576: 2564: 2553: 2524: 2503: 2485: 2476:(6): 1713–1733. 2464: 2446: 2425: 2415: 2394: 2377:(6): 1255–1278. 2365: 2344: 2326: 2297: 2287: 2258: 2248: 2223: 2194: 2153: 2116: 2090: 2080: 2059: 2033: 2023: 2005: 1995: 1961: 1951: 1933: 1912: 1910: 1884: 1874: 1853: 1835: 1825: 1807: 1797: 1779: 1770:(5): 1089–1122. 1758: 1748: 1722: 1712: 1694: 1684: 1658: 1648: 1622: 1612: 1594: 1573: 1544: 1518: 1508: 1478: 1230:no-trade theorem 1105:Lincoln Electric 1085:Topkis's theorem 876:Envelope Theorem 818:Nash equilibrium 737:normal-form game 721:Topkis's Theorem 670:Robert B. Wilson 631:Robert B. Wilson 592:He won the 2012 493:Robert B. Wilson 388:no-trade theorem 377:Robert B. Wilson 375:, together with 367:, specifically 304:Gillian Hadfield 282:Robert B. Wilson 277:Doctoral advisor 271: 170:Incentive theory 118: 114: 112: 97: 83: 82: 74: 67: 63: 60: 54: 51:inline citations 27: 26: 19: 7795: 7794: 7790: 7789: 7788: 7786: 7785: 7784: 7690: 7689: 7688: 7683: 7617: 7603:max^n algorithm 7576: 7572:William Vickrey 7532:Reinhard Selten 7487:Kenneth Binmore 7402:David K. Levine 7397:Daniel Kahneman 7364: 7358: 7334:Negamax theorem 7324:Minimax theorem 7302: 7263:Diner's dilemma 7118:All-pay auction 7084: 7070:Stochastic game 7022:Mean-field game 6993: 6986: 6957:Markov strategy 6893: 6759: 6751: 6722:Sequential game 6707:Information set 6692:Game complexity 6662:Congestion game 6650: 6644: 6614: 6609: 6601: 6592:Douglas Diamond 6582: 6563: 6548: 6529: 6517: 6509: 6504:Bengt Holmström 6497: 6489: 6481: 6465: 6453: 6441: 6425: 6413: 6405: 6389: 6381: 6369: 6360:Finn E. Kydland 6357: 6345: 6340:Vernon L. Smith 6336:Daniel Kahneman 6333: 6317: 6306: 6294: 6286: 6278: 6266: 6261:William Vickrey 6254: 6246: 6241:Reinhard Selten 6230: 6221:Robert W. Fogel 6218: 6210: 6205:Ronald H. Coase 6202: 6186: 6181:Trygve Haavelmo 6178: 6170: 6165:Robert M. Solow 6162: 6154: 6146: 6138: 6130: 6122: 6114: 6106: 6094: 6086: 6074: 6069:Milton Friedman 6066: 6055: 6043: 6031: 6023: 6011: 6003: 5995: 5983: 5972: 5963: 5933: 5928: 5871: 5863: 5860:(United States) 5854:(United States) 5833: 5830:(United States) 5828:Charles M. Rice 5818:(United States) 5816:Harvey J. Alter 5797: 5794:(United States) 5786:Reinhard Genzel 5766: 5747: 5746:(United States) 5727: 5724:(United States) 5722:Jennifer Doudna 5702: 5695: 5623: 5622: 5619: 5614: 5613: 5606: 5602: 5592: 5590: 5582: 5578: 5577: 5573: 5565: 5561: 5560: 5556: 5543: 5542: 5538: 5528: 5526: 5515: 5514: 5510: 5497: 5493: 5484: 5480: 5472: 5468: 5455: 5454: 5450: 5445: 5441: 5436: 5432: 5427: 5423: 5418: 5414: 5409: 5405: 5381:10.1.1.422.8639 5364: 5357: 5314: 5307: 5299: 5295: 5286: 5282: 5251: 5247: 5216: 5212: 5181: 5177: 5154: 5150: 5111: 5107: 5102: 5098: 5092: 5088: 5056:10.1.1.124.8019 5039: 5035: 4996: 4992: 4951: 4947: 4908: 4904: 4896: 4889: 4885: 4884: 4880: 4866:Folbre, Nancy " 4865: 4861: 4853: 4849: 4841: 4837: 4792: 4788: 4779: 4777: 4775: 4749: 4745: 4714: 4710: 4675: 4671: 4634: 4630: 4625: 4621: 4616: 4612: 4603: 4599: 4590: 4586: 4576: 4574: 4567: 4561: 4557: 4516: 4512: 4508:, Stanford GSB. 4503: 4499: 4474:10.2307/2951505 4468:(5): 997–1039. 4458: 4454: 4407: 4403: 4396: 4380: 4376: 4341: 4337: 4327: 4325: 4317: 4316: 4312: 4299: 4298: 4294: 4284: 4282: 4277: 4276: 4272: 4262: 4260: 4251: 4250: 4246: 4236: 4234: 4230: 4229: 4225: 4215: 4213: 4204: 4203: 4199: 4189: 4187: 4183: 4179: 4178: 4174: 4164: 4162: 4153: 4152: 4148: 4135: 4134: 4130: 4120: 4118: 4113: 4112: 4108: 4098: 4096: 4091: 4090: 4086: 4077: 4073: 4063: 4061: 4053: 4052: 4048: 4038: 4036: 4028: 4027: 4023: 4013: 4011: 4003: 4002: 3998: 3988: 3986: 3982: 3981: 3977: 3967: 3965: 3959:"Robert Wilson" 3957: 3956: 3952: 3942: 3940: 3933: 3929: 3928: 3924: 3914: 3912: 3904: 3903: 3894: 3863: 3859: 3849: 3847: 3839: 3838: 3831: 3821: 3819: 3817:The Nobel Prize 3811: 3810: 3806: 3796: 3794: 3786: 3785: 3781: 3771: 3769: 3759: 3755: 3745: 3743: 3741:The Jewish News 3733: 3729: 3719: 3717: 3708: 3707: 3703: 3694: 3693: 3689: 3681: 3674: 3665: 3664: 3657: 3647: 3645: 3633: 3629: 3621: 3617: 3616: 3609: 3599: 3597: 3589: 3588: 3584: 3579: 3567: 3548:10.1.1.649.5582 3482:10.1.1.727.1750 3443:10.1.1.151.6989 3404:10.1.1.727.4004 3373:10.1.1.497.9686 3342:10.1.1.487.2981 3303:10.1.1.529.9950 3256:10.1.1.516.6267 3155: 3136:10.1.1.120.7158 3109: 3108: 3104: 3044: 3000:10.1.1.217.4736 2953:10.1.1.528.8990 2906:10.1.1.195.7314 2685:10.2307/2951479 2590:Meyer, Margaret 2573: 2536:(100): 82–100. 2492:10.2307/2938286 2483:10.1.1.295.1370 2444:10.1.1.715.3715 2413:10.1.1.669.1678 2383:10.2307/2938316 2212:10.2307/3440309 2105:10.2307/1884213 2088: 2048:10.2307/1913238 2031: 2003: 1959: 1882: 1833: 1805: 1786:10.2307/1911865 1777:10.1.1.186.4633 1720: 1692: 1656: 1637:10.2307/1912637 1620: 1601:10.2307/3003562 1592:10.1.1.465.6331 1562:10.2307/1912511 1533:10.2307/1911137 1516: 1497:10.2307/1910414 1469: 1406: 1365: 1352: 1284: 1279: 1270:efficiency wage 1254: 1226: 1221: 1173: 1137:Joseph Stiglitz 1129: 1097:Bengt Holmstrom 1072: 1035: 988:Brownian motion 976:Bengt Holmstrom 972: 967: 952:matching theory 928: 922: 831: 803: 781: 768: 751: 733: 717: 699: 686:Robert J. Weber 682: 658: 649: 570: 558:William Vickrey 525:Yale University 505:Robert J. Weber 497:Bengt Holmstrom 481: 479:Academic career 443:in 1970 with a 422: 381:auction formats 326:Academic career 306: 302: 298: 294: 269: 249: 246:Yale University 244: 207: 202: 197: 172: 168: 145: 129: 119: 116: 110: 108: 100: 99:Milgrom in 2013 88: 75: 64: 58: 55: 40: 28: 24: 17: 12: 11: 5: 7793: 7783: 7782: 7777: 7772: 7767: 7762: 7757: 7752: 7747: 7742: 7737: 7732: 7730:Game theorists 7727: 7722: 7717: 7712: 7707: 7702: 7685: 7684: 7682: 7681: 7676: 7671: 7666: 7661: 7656: 7651: 7646: 7641: 7636: 7631: 7625: 7623: 7619: 7618: 7616: 7615: 7610: 7605: 7600: 7595: 7590: 7584: 7582: 7578: 7577: 7575: 7574: 7569: 7564: 7559: 7554: 7549: 7544: 7539: 7537:Robert Axelrod 7534: 7529: 7524: 7519: 7514: 7512:Olga Bondareva 7509: 7504: 7502:Melvin Dresher 7499: 7494: 7492:Leonid Hurwicz 7489: 7484: 7479: 7474: 7469: 7464: 7459: 7454: 7449: 7444: 7439: 7434: 7429: 7427:Harold W. Kuhn 7424: 7419: 7417:Drew Fudenberg 7414: 7409: 7407:David M. Kreps 7404: 7399: 7394: 7392:Claude Shannon 7389: 7384: 7379: 7374: 7368: 7366: 7360: 7359: 7357: 7356: 7351: 7346: 7341: 7336: 7331: 7329:Nash's theorem 7326: 7321: 7316: 7310: 7308: 7304: 7303: 7301: 7300: 7295: 7290: 7285: 7280: 7275: 7270: 7265: 7260: 7255: 7250: 7245: 7240: 7235: 7230: 7225: 7220: 7215: 7210: 7205: 7200: 7195: 7190: 7188:Ultimatum game 7185: 7180: 7175: 7170: 7168:Dollar auction 7165: 7160: 7155: 7153:Centipede game 7150: 7145: 7140: 7135: 7130: 7125: 7120: 7115: 7110: 7108:Infinite chess 7105: 7100: 7094: 7092: 7086: 7085: 7083: 7082: 7077: 7075:Symmetric game 7072: 7067: 7062: 7060:Signaling game 7057: 7055:Screening game 7052: 7047: 7045:Potential game 7042: 7037: 7032: 7024: 7019: 7014: 7009: 7004: 6998: 6996: 6988: 6987: 6985: 6984: 6979: 6974: 6972:Mixed strategy 6969: 6964: 6959: 6954: 6949: 6944: 6939: 6934: 6929: 6924: 6919: 6914: 6909: 6903: 6901: 6895: 6894: 6892: 6891: 6886: 6881: 6876: 6871: 6866: 6861: 6856: 6854:Risk dominance 6851: 6846: 6841: 6836: 6831: 6826: 6821: 6816: 6811: 6806: 6801: 6796: 6791: 6786: 6781: 6776: 6771: 6765: 6763: 6753: 6752: 6750: 6749: 6744: 6739: 6734: 6729: 6724: 6719: 6714: 6709: 6704: 6699: 6697:Graphical game 6694: 6689: 6684: 6679: 6674: 6669: 6664: 6658: 6656: 6652: 6651: 6643: 6642: 6635: 6628: 6620: 6611: 6610: 6608: 6607: 6604:Claudia Goldin 6599: 6580: 6573:Joshua Angrist 6561: 6546: 6543:Michael Kremer 6527: 6515: 6507: 6495: 6487: 6479: 6468:Eugene F. Fama 6463: 6451: 6439: 6423: 6411: 6403: 6396:Eric S. Maskin 6392:Leonid Hurwicz 6387: 6379: 6367: 6355: 6343: 6331: 6314: 6312: 6308: 6307: 6305: 6304: 6292: 6284: 6276: 6264: 6252: 6244: 6228: 6216: 6213:Gary S. Becker 6208: 6200: 6184: 6176: 6173:Maurice Allais 6168: 6160: 6152: 6144: 6136: 6128: 6120: 6112: 6104: 6092: 6084: 6081:James E. Meade 6072: 6063: 6061: 6057: 6056: 6054: 6053: 6041: 6029: 6021: 6009: 6001: 5993: 5980: 5978: 5974: 5973: 5962: 5961: 5954: 5947: 5939: 5930: 5929: 5927: 5926: 5921: 5916: 5911: 5906: 5901: 5896: 5891: 5886: 5881: 5876: 5868: 5865: 5864: 5862: 5861: 5855: 5848: 5846: 5835: 5834: 5832: 5831: 5825: 5819: 5812: 5810: 5799: 5798: 5796: 5795: 5792:Andrea M. Ghez 5789: 5783: 5776: 5774: 5768: 5767: 5762: 5760: 5749: 5748: 5742: 5740: 5729: 5728: 5726: 5725: 5719: 5712: 5710: 5704: 5703: 5694: 5693: 5686: 5679: 5671: 5665: 5664: 5655: 5649: 5638: 5636:Google Scholar 5629: 5618: 5617:External links 5615: 5612: 5611: 5600: 5571: 5554: 5536: 5508: 5491: 5478: 5466: 5448: 5439: 5430: 5421: 5412: 5403: 5355: 5305: 5293: 5280: 5261:(3): 315–328. 5245: 5226:(1): 257–276. 5210: 5191:(2): 365–394. 5175: 5164:(2): 378–405. 5148: 5127:10.1086/466995 5121:(3): 461–483. 5105: 5096: 5086: 5065:10.1086/260231 5049:(4): 729–754. 5033: 5012:10.1086/259630 5006:(2): 311–329. 4990: 4968:10.1.1.322.325 4961:(2): 253–279. 4945: 4924:10.1086/466547 4902: 4878: 4859: 4847: 4835: 4806:(2): 311–320. 4786: 4773: 4753:"Introduction" 4743: 4730:10.1086/261948 4724:(3): 607–615. 4708: 4689:(1): 187–223. 4669: 4648:(2): 219–238. 4628: 4619: 4610: 4597: 4584: 4555: 4526:(3): 305–321. 4510: 4497: 4452: 4423:(4): 619–632. 4401: 4394: 4374: 4355:(2): 245–252. 4335: 4323:NobelPrize.org 4310: 4305:www.aeaweb.org 4292: 4270: 4244: 4223: 4197: 4172: 4146: 4128: 4106: 4084: 4071: 4046: 4021: 3996: 3975: 3950: 3938:UCLA Economics 3922: 3892: 3857: 3841:"Paul Milgrom" 3829: 3804: 3788:"Paul Milgrom" 3779: 3753: 3727: 3701: 3687: 3672: 3667:"Auctionomics" 3655: 3627: 3607: 3581: 3580: 3578: 3575: 3574: 3573: 3566: 3563: 3562: 3561: 3541:(2): 585–623. 3530: 3510:(2): 311–320. 3495: 3475:(2): 603–607. 3464: 3425: 3397:(3): 160–185. 3386: 3366:(1): 212–247. 3355: 3324: 3285: 3238: 3218:(2): 115–131. 3203: 3183:(4): 935–965. 3168: 3159: 3153: 3122: 3102: 3081: 3063:(4): 913–935. 3048: 3042: 3029: 2993:(2): 583–601. 2982: 2935: 2915:10.1086/262118 2899:(2): 245–272. 2888: 2853: 2841:(1): 173–179. 2826: 2816:(1): 113–128. 2805: 2795:(4): 997–999. 2784: 2755: 2735:10.1086/261953 2729:(4): 745–776. 2718: 2708:(4): 972–991. 2697: 2679:(1): 157–180. 2668: 2658:(3): 441–459. 2647: 2627:10.1086/261948 2621:(3): 607–615. 2610: 2586: 2577: 2572:978-0132246507 2571: 2554: 2525: 2504: 2465: 2426: 2395: 2366: 2345: 2298: 2270:(1): 154–159. 2259: 2224: 2206:(3): 275–289. 2195: 2175:10.1086/261523 2154: 2134:10.1086/228945 2117: 2099:(3): 453–476. 2081: 2071:(2): 184–193. 2060: 2042:(2): 303–328. 2024: 1996: 1976:10.1086/261408 1970:(4): 796–821. 1952: 1931:10.1.1.460.947 1913: 1875: 1865:(2): 305–309. 1854: 1844:(2): 161–169. 1826: 1816:(2): 245‑252. 1798: 1759: 1713: 1685: 1667:(2): 280–312. 1649: 1613: 1574: 1556:(4): 921–943. 1545: 1527:(1): 219–222. 1509: 1480: 1468: 1465: 1457: 1456: 1418:Jonathan Levin 1405: 1402: 1381:Jonathan Levin 1364: 1361: 1351: 1348: 1336:winner's curse 1299:Preston McAfee 1283: 1280: 1278: 1275: 1253: 1250: 1225: 1222: 1220: 1217: 1177:Douglass North 1172: 1169: 1141:Michael Spence 1133:George Akerlof 1128: 1125: 1113:Margaret Meyer 1071: 1068: 1055:winner's curse 1034: 1031: 1018:New York Times 971: 968: 966: 963: 946:auction theory 924:Main article: 921: 918: 892:Voting paradox 868:Paul Samuelson 860:lattice theory 830: 827: 799: 777: 764: 747: 743:, is denoted { 732: 729: 716: 713: 698: 697:Repeated games 695: 681: 678: 662:David M. Kreps 657: 654: 648: 645: 639:private values 569: 566: 480: 477: 471:in 1978 and a 457:Columbus, Ohio 421: 418: 369:auction theory 347: 346: 343: 342: 339: 338: 328: 327: 323: 322: 319: 318: 315: 314: 311: 310: 289: 285: 284: 279: 273: 272: 261: 255: 254: 253:(1987–present) 238: 234: 233: 228: 224: 223: 217: 216: 191: 187: 186: 181: 177: 176: 166:Auction theory 163: 162:Known for 159: 158: 135: 131: 130: 120: 115:April 20, 1948 106: 102: 101: 98: 90: 89: 86: 77: 76: 31: 29: 22: 15: 9: 6: 4: 3: 2: 7792: 7781: 7778: 7776: 7773: 7771: 7768: 7766: 7763: 7761: 7758: 7756: 7755:Living people 7753: 7751: 7748: 7746: 7743: 7741: 7738: 7736: 7733: 7731: 7728: 7726: 7723: 7721: 7718: 7716: 7713: 7711: 7708: 7706: 7703: 7701: 7698: 7697: 7695: 7680: 7677: 7675: 7672: 7670: 7667: 7665: 7662: 7660: 7657: 7655: 7652: 7650: 7647: 7645: 7642: 7640: 7637: 7635: 7632: 7630: 7627: 7626: 7624: 7622:Miscellaneous 7620: 7614: 7611: 7609: 7606: 7604: 7601: 7599: 7596: 7594: 7591: 7589: 7586: 7585: 7583: 7579: 7573: 7570: 7568: 7565: 7563: 7560: 7558: 7557:Samuel Bowles 7555: 7553: 7552:Roger Myerson 7550: 7548: 7545: 7543: 7542:Robert Aumann 7540: 7538: 7535: 7533: 7530: 7528: 7525: 7523: 7520: 7518: 7515: 7513: 7510: 7508: 7505: 7503: 7500: 7498: 7497:Lloyd Shapley 7495: 7493: 7490: 7488: 7485: 7483: 7482:Kenneth Arrow 7480: 7478: 7475: 7473: 7470: 7468: 7465: 7463: 7462:John Harsanyi 7460: 7458: 7455: 7453: 7450: 7448: 7445: 7443: 7440: 7438: 7435: 7433: 7432:Herbert Simon 7430: 7428: 7425: 7423: 7420: 7418: 7415: 7413: 7410: 7408: 7405: 7403: 7400: 7398: 7395: 7393: 7390: 7388: 7385: 7383: 7380: 7378: 7375: 7373: 7370: 7369: 7367: 7361: 7355: 7352: 7350: 7347: 7345: 7342: 7340: 7337: 7335: 7332: 7330: 7327: 7325: 7322: 7320: 7317: 7315: 7312: 7311: 7309: 7305: 7299: 7296: 7294: 7291: 7289: 7286: 7284: 7281: 7279: 7276: 7274: 7271: 7269: 7266: 7264: 7261: 7259: 7256: 7254: 7251: 7249: 7246: 7244: 7241: 7239: 7236: 7234: 7233:Fair division 7231: 7229: 7226: 7224: 7221: 7219: 7216: 7214: 7211: 7209: 7208:Dictator game 7206: 7204: 7201: 7199: 7196: 7194: 7191: 7189: 7186: 7184: 7181: 7179: 7176: 7174: 7171: 7169: 7166: 7164: 7161: 7159: 7156: 7154: 7151: 7149: 7146: 7144: 7141: 7139: 7136: 7134: 7131: 7129: 7126: 7124: 7121: 7119: 7116: 7114: 7111: 7109: 7106: 7104: 7101: 7099: 7096: 7095: 7093: 7091: 7087: 7081: 7080:Zero-sum game 7078: 7076: 7073: 7071: 7068: 7066: 7063: 7061: 7058: 7056: 7053: 7051: 7050:Repeated game 7048: 7046: 7043: 7041: 7038: 7036: 7033: 7031: 7029: 7025: 7023: 7020: 7018: 7015: 7013: 7010: 7008: 7005: 7003: 7000: 6999: 6997: 6995: 6989: 6983: 6980: 6978: 6975: 6973: 6970: 6968: 6967:Pure strategy 6965: 6963: 6960: 6958: 6955: 6953: 6950: 6948: 6945: 6943: 6940: 6938: 6935: 6933: 6932:De-escalation 6930: 6928: 6925: 6923: 6920: 6918: 6915: 6913: 6910: 6908: 6905: 6904: 6902: 6900: 6896: 6890: 6887: 6885: 6882: 6880: 6877: 6875: 6874:Shapley value 6872: 6870: 6867: 6865: 6862: 6860: 6857: 6855: 6852: 6850: 6847: 6845: 6842: 6840: 6837: 6835: 6832: 6830: 6827: 6825: 6822: 6820: 6817: 6815: 6812: 6810: 6807: 6805: 6802: 6800: 6797: 6795: 6792: 6790: 6787: 6785: 6782: 6780: 6777: 6775: 6772: 6770: 6767: 6766: 6764: 6762: 6758: 6754: 6748: 6745: 6743: 6742:Succinct game 6740: 6738: 6735: 6733: 6730: 6728: 6725: 6723: 6720: 6718: 6715: 6713: 6710: 6708: 6705: 6703: 6700: 6698: 6695: 6693: 6690: 6688: 6685: 6683: 6680: 6678: 6675: 6673: 6670: 6668: 6665: 6663: 6660: 6659: 6657: 6653: 6649: 6641: 6636: 6634: 6629: 6627: 6622: 6621: 6618: 6605: 6600: 6597: 6593: 6589: 6585: 6581: 6578: 6574: 6570: 6566: 6562: 6559: 6555: 6551: 6547: 6544: 6540: 6536: 6532: 6528: 6525: 6521: 6516: 6513: 6508: 6505: 6501: 6496: 6493: 6488: 6485: 6480: 6477: 6473: 6469: 6464: 6461: 6457: 6456:Alvin E. Roth 6452: 6449: 6445: 6440: 6437: 6433: 6429: 6424: 6421: 6417: 6416:Elinor Ostrom 6412: 6409: 6404: 6401: 6397: 6393: 6388: 6385: 6380: 6377: 6373: 6368: 6365: 6361: 6356: 6353: 6349: 6344: 6341: 6337: 6332: 6329: 6325: 6321: 6316: 6315: 6313: 6309: 6302: 6298: 6293: 6290: 6285: 6282: 6277: 6274: 6270: 6265: 6262: 6258: 6253: 6250: 6245: 6242: 6238: 6234: 6229: 6226: 6222: 6217: 6214: 6209: 6206: 6201: 6198: 6194: 6190: 6185: 6182: 6177: 6174: 6169: 6166: 6161: 6158: 6153: 6150: 6145: 6142: 6141:Richard Stone 6137: 6134: 6133:Gérard Debreu 6129: 6126: 6121: 6118: 6113: 6110: 6105: 6102: 6098: 6093: 6090: 6085: 6082: 6078: 6073: 6070: 6065: 6064: 6062: 6058: 6051: 6047: 6042: 6039: 6035: 6034:Gunnar Myrdal 6030: 6027: 6022: 6019: 6015: 6014:John R. Hicks 6010: 6007: 6006:Simon Kuznets 6002: 5999: 5994: 5991: 5990:Jan Tinbergen 5987: 5986:Ragnar Frisch 5982: 5981: 5979: 5975: 5971: 5967: 5960: 5955: 5953: 5948: 5946: 5941: 5940: 5937: 5925: 5922: 5920: 5917: 5915: 5912: 5910: 5907: 5905: 5902: 5900: 5897: 5895: 5892: 5890: 5887: 5885: 5882: 5880: 5877: 5874: 5870: 5869: 5866: 5859: 5856: 5853: 5850: 5849: 5847: 5844: 5840: 5836: 5829: 5826: 5823: 5820: 5817: 5814: 5813: 5811: 5808: 5804: 5800: 5793: 5790: 5787: 5784: 5781: 5780:Roger Penrose 5778: 5777: 5775: 5773: 5769: 5765: 5761: 5758: 5754: 5750: 5745: 5741: 5738: 5734: 5730: 5723: 5720: 5717: 5714: 5713: 5711: 5709: 5705: 5700: 5692: 5687: 5685: 5680: 5678: 5673: 5672: 5669: 5662: 5659: 5656: 5653: 5650: 5647: 5642: 5639: 5637: 5633: 5630: 5626: 5621: 5620: 5609: 5604: 5588: 5581: 5575: 5564: 5558: 5550: 5546: 5540: 5524: 5523: 5522:The Economist 5518: 5512: 5505: 5501: 5495: 5489:", June 2004. 5488: 5482: 5475: 5470: 5462: 5458: 5452: 5443: 5434: 5425: 5416: 5407: 5399: 5395: 5391: 5387: 5382: 5377: 5373: 5369: 5362: 5360: 5351: 5347: 5343: 5339: 5335: 5331: 5327: 5323: 5319: 5312: 5310: 5302: 5297: 5290: 5284: 5276: 5272: 5268: 5264: 5260: 5256: 5249: 5241: 5237: 5233: 5229: 5225: 5221: 5214: 5206: 5202: 5198: 5194: 5190: 5186: 5179: 5171: 5167: 5163: 5159: 5152: 5144: 5140: 5136: 5132: 5128: 5124: 5120: 5116: 5109: 5100: 5090: 5082: 5078: 5074: 5070: 5066: 5062: 5057: 5052: 5048: 5044: 5037: 5029: 5025: 5021: 5017: 5013: 5009: 5005: 5001: 4994: 4986: 4982: 4978: 4974: 4969: 4964: 4960: 4956: 4949: 4941: 4937: 4933: 4929: 4925: 4921: 4917: 4913: 4906: 4895: 4888: 4882: 4875: 4874: 4869: 4863: 4856: 4851: 4845: 4839: 4831: 4827: 4823: 4819: 4814: 4809: 4805: 4801: 4797: 4790: 4776: 4770: 4766: 4762: 4758: 4754: 4747: 4739: 4735: 4731: 4727: 4723: 4719: 4712: 4704: 4700: 4696: 4692: 4688: 4684: 4680: 4673: 4665: 4661: 4656: 4651: 4647: 4643: 4639: 4632: 4623: 4614: 4607: 4601: 4594: 4588: 4573: 4566: 4559: 4551: 4547: 4542: 4537: 4533: 4529: 4525: 4521: 4514: 4507: 4501: 4493: 4489: 4484: 4479: 4475: 4471: 4467: 4463: 4456: 4448: 4444: 4439: 4434: 4430: 4426: 4422: 4418: 4417: 4412: 4405: 4397: 4391: 4387: 4386: 4378: 4370: 4366: 4362: 4358: 4354: 4350: 4346: 4339: 4324: 4320: 4314: 4306: 4302: 4296: 4280: 4274: 4258: 4254: 4248: 4233: 4227: 4211: 4207: 4201: 4182: 4176: 4160: 4156: 4150: 4142: 4138: 4132: 4116: 4110: 4094: 4088: 4081: 4075: 4060: 4056: 4050: 4035: 4031: 4025: 4010: 4006: 4000: 3985: 3979: 3964: 3960: 3954: 3939: 3932: 3926: 3911: 3907: 3901: 3899: 3897: 3888: 3884: 3880: 3876: 3872: 3868: 3861: 3846: 3842: 3836: 3834: 3818: 3814: 3808: 3793: 3789: 3783: 3768: 3764: 3757: 3742: 3738: 3731: 3715: 3711: 3705: 3697: 3691: 3684: 3679: 3677: 3668: 3662: 3660: 3644: 3643: 3638: 3631: 3620: 3614: 3612: 3596: 3592: 3586: 3582: 3572: 3569: 3568: 3558: 3554: 3549: 3544: 3540: 3536: 3531: 3527: 3523: 3518: 3513: 3509: 3505: 3501: 3496: 3492: 3488: 3483: 3478: 3474: 3470: 3465: 3461: 3457: 3453: 3449: 3444: 3439: 3435: 3431: 3426: 3422: 3418: 3414: 3410: 3405: 3400: 3396: 3392: 3387: 3383: 3379: 3374: 3369: 3365: 3361: 3356: 3352: 3348: 3343: 3338: 3335:(2): 95–113. 3334: 3330: 3325: 3321: 3317: 3313: 3309: 3304: 3299: 3295: 3291: 3286: 3282: 3278: 3274: 3270: 3266: 3262: 3257: 3252: 3248: 3244: 3239: 3235: 3231: 3226: 3221: 3217: 3213: 3209: 3204: 3200: 3196: 3191: 3186: 3182: 3178: 3174: 3169: 3165: 3160: 3156: 3154:9780262033428 3150: 3146: 3142: 3137: 3132: 3128: 3123: 3119: 3113: 3105: 3099: 3095: 3091: 3088:. MIT Press. 3087: 3082: 3078: 3074: 3070: 3066: 3062: 3058: 3054: 3049: 3045: 3039: 3035: 3030: 3026: 3022: 3018: 3014: 3010: 3006: 3001: 2996: 2992: 2988: 2983: 2979: 2975: 2971: 2967: 2963: 2959: 2954: 2949: 2945: 2941: 2936: 2932: 2928: 2924: 2920: 2916: 2912: 2907: 2902: 2898: 2894: 2889: 2885: 2881: 2876: 2871: 2867: 2863: 2859: 2854: 2849: 2844: 2840: 2836: 2832: 2827: 2823: 2819: 2815: 2811: 2806: 2802: 2798: 2794: 2790: 2785: 2781: 2777: 2773: 2769: 2765: 2761: 2756: 2752: 2748: 2744: 2740: 2736: 2732: 2728: 2724: 2719: 2715: 2711: 2707: 2703: 2698: 2694: 2690: 2686: 2682: 2678: 2674: 2669: 2665: 2661: 2657: 2653: 2648: 2644: 2640: 2636: 2632: 2628: 2624: 2620: 2616: 2611: 2607: 2603: 2599: 2595: 2591: 2587: 2583: 2578: 2574: 2568: 2563: 2562: 2555: 2551: 2547: 2543: 2539: 2535: 2531: 2526: 2522: 2518: 2514: 2510: 2505: 2501: 2497: 2493: 2489: 2484: 2479: 2475: 2471: 2466: 2462: 2458: 2454: 2450: 2445: 2440: 2436: 2432: 2427: 2423: 2419: 2414: 2409: 2405: 2401: 2396: 2392: 2388: 2384: 2380: 2376: 2372: 2367: 2363: 2359: 2356:(3): 511–28. 2355: 2351: 2346: 2342: 2338: 2334: 2330: 2325: 2320: 2316: 2312: 2308: 2304: 2299: 2295: 2291: 2286: 2281: 2277: 2273: 2269: 2265: 2260: 2256: 2252: 2247: 2242: 2238: 2234: 2230: 2225: 2221: 2217: 2213: 2209: 2205: 2201: 2196: 2192: 2188: 2184: 2180: 2176: 2172: 2168: 2164: 2160: 2155: 2151: 2147: 2143: 2139: 2135: 2131: 2128:: S154–S179. 2127: 2123: 2118: 2114: 2110: 2106: 2102: 2098: 2094: 2087: 2082: 2078: 2074: 2070: 2066: 2061: 2057: 2053: 2049: 2045: 2041: 2037: 2030: 2025: 2021: 2017: 2013: 2009: 2002: 1997: 1993: 1989: 1985: 1981: 1977: 1973: 1969: 1965: 1958: 1953: 1949: 1945: 1941: 1937: 1932: 1927: 1924:(1): 71‑100. 1923: 1919: 1914: 1909: 1904: 1900: 1896: 1893:(4): 619–32. 1892: 1888: 1881: 1876: 1872: 1868: 1864: 1860: 1855: 1851: 1847: 1843: 1839: 1832: 1827: 1823: 1819: 1815: 1811: 1804: 1799: 1795: 1791: 1787: 1783: 1778: 1773: 1769: 1765: 1760: 1756: 1752: 1747: 1742: 1738: 1734: 1731:(1): 105–14. 1730: 1726: 1719: 1714: 1710: 1706: 1702: 1698: 1691: 1686: 1682: 1678: 1674: 1670: 1666: 1662: 1655: 1650: 1646: 1642: 1638: 1634: 1631:(2): 443–59. 1630: 1626: 1619: 1614: 1610: 1606: 1602: 1598: 1593: 1588: 1585:(2): 380–91. 1584: 1580: 1575: 1571: 1567: 1563: 1559: 1555: 1551: 1546: 1542: 1538: 1534: 1530: 1526: 1522: 1515: 1510: 1506: 1502: 1498: 1494: 1491:(3): 679–88. 1490: 1486: 1481: 1476: 1471: 1470: 1464: 1461: 1453: 1452: 1451: 1448: 1444: 1440: 1434: 1429: 1427: 1423: 1419: 1415: 1410: 1400: 1394: 1388: 1384: 1382: 1376: 1374: 1373:Alvin E. Roth 1370: 1360: 1356: 1347: 1345: 1341: 1337: 1331: 1327: 1322: 1317: 1314: 1310: 1306: 1304: 1303:John McMillan 1300: 1295: 1291: 1289: 1274: 1271: 1267: 1262: 1259: 1252:Labor markets 1249: 1245: 1243: 1237: 1234: 1231: 1216: 1214: 1208: 1206: 1201: 1199: 1195: 1191: 1186: 1183: 1178: 1168: 1164: 1160: 1156: 1152: 1148: 1144: 1142: 1138: 1134: 1124: 1122: 1117: 1114: 1108: 1106: 1100: 1098: 1093: 1088: 1086: 1080: 1077: 1067: 1064: 1058: 1056: 1052: 1048: 1044: 1040: 1029: 1027: 1021: 1019: 1013: 1011: 1003: 999: 996: 991: 989: 986:-dimensional 985: 979: 977: 970:Agency theory 962: 960: 959: 954: 953: 948: 947: 940: 935: 933: 932:Market Design 927: 926:Market design 920:Market design 916: 911: 906: 903: 901: 897: 893: 889: 884: 882: 877: 873: 869: 865: 861: 857: 853: 849: 843: 841: 835: 826: 823: 819: 814: 811: 807: 802: 798: 793: 789: 785: 780: 776: 772: 767: 763: 759: 755: 750: 746: 742: 738: 728: 724: 722: 712: 709: 705: 694: 691: 690:Bayesian game 687: 677: 675: 671: 667: 663: 653: 643: 640: 634: 632: 628: 623: 621: 616: 612: 606: 601: 598: 595: 589: 584: 581: 579: 575: 565: 563: 559: 555: 551: 547: 546: 541: 540: 535: 534: 528: 526: 522: 517: 513: 510: 506: 502: 498: 494: 490: 489:Roger Myerson 486: 476: 474: 470: 466: 462: 458: 454: 453:San Francisco 450: 446: 442: 437: 435: 431: 427: 417: 414: 412: 407: 405: 401: 397: 393: 389: 384: 382: 378: 374: 370: 366: 361: 357: 353: 344: 340: 337: 333: 329: 324: 320: 316: 312: 309: 305: 301: 297: 293: 290: 286: 283: 280: 278: 274: 267: 266: 262: 260: 256: 252: 247: 242: 239: 235: 232: 229: 225: 222: 218: 214: 210: 205: 200: 195: 192: 188: 185: 184:Eva Meyersson 182: 178: 175: 174:Market design 171: 167: 164: 160: 156: 152: 148: 143: 139: 136: 132: 127: 123: 117:(age 76) 107: 103: 96: 91: 84: 81: 73: 70: 62: 52: 48: 44: 38: 37: 32:This article 30: 21: 20: 7527:Peyton Young 7522:Paul Milgrom 7521: 7437:Hervé Moulin 7377:Amos Tversky 7319:Folk theorem 7030:-player game 7027: 6952:Grim trigger 6588:Ben Bernanke 6577:Guido Imbens 6554:Paul Milgrom 6553: 6539:Esther Duflo 6492:Angus Deaton 6408:Paul Krugman 6311:2001–present 6077:Bertil Ohlin 5903: 5852:Paul Milgrom 5851: 5744:Louise Glück 5660: 5641:Paul Milgrom 5632:Paul Milgrom 5603: 5591:. 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CME Group 4165:October 18, 4064:October 18, 4039:October 18, 4014:October 18, 3968:October 18, 3943:October 18, 3915:October 18, 3850:October 12, 3822:December 2, 3797:October 18, 3772:October 18, 3767:Jewish News 3746:October 12, 3720:February 7, 3648:October 12, 2600:(1): 9–35. 2437:: 303–328. 2406:(1): 1–23. 2309:(2): 1–31. 2239:(3): 3–22. 1190:Avner Greif 900:Susan Athey 888:Joshua Gans 647:Game theory 449:mathematics 365:game theory 332:Information 300:Joshua Gans 296:Luís Cabral 292:Susan Athey 248:(1982–1987) 243:(1979–1983) 7694:Categories 7288:Trust game 7273:Kuhn poker 6942:Escalation 6937:Deterrence 6927:Cheap talk 6899:Strategies 6717:Preference 6646:Topics of 6569:David Card 6524:Paul Romer 5733:Literature 3577:References 2584:: 195–216. 1155:pricing). 934:this way: 521:management 469:statistics 308:Li Shengwu 111:1948-04-20 59:April 2018 43:improve it 7472:John Nash 7178:Stag hunt 6922:Collusion 6060:1976–2000 5977:1969–1975 5966:Laureates 5788:(Germany) 5708:Chemistry 5701:laureates 5376:CiteSeerX 5342:0002-8282 5275:0144-8188 5081:154829661 5051:CiteSeerX 5028:155053131 4985:0022-0531 4963:CiteSeerX 4940:153539977 4830:153765277 4822:1465-7295 4738:153568621 4664:0047-2727 4550:0304-4068 4447:0364-765X 4369:0022-0531 4216:April 16, 4117:. 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