3431:, a person who only cares about expected values of a gamble would pay an arbitrarily large finite amount to take this gamble. However, this experiment demonstrated that there is no upper bound on the potential rewards from very low probability events. In the hypothetical setup, a person flips a coin repeatedly. The participant's prize is determined by the number of times the coin lands on heads consecutively. For every time the coin comes up heads (1/2 probability), the participant's prize is doubled. The game ends when the participant flips the coin and it comes out tails. A player who only cares about expected value of the payoff should be willing to pay any finite amount of money to play because this entry cost will always be less than the expected, infinite, value of the game. However, in reality, people do not do this. "Only a few of the participants were willing to pay a maximum of $ 25 to enter the game because many of them were risk averse and unwilling to bet on a very small possibility at a very high price.
428:, an American statistician, derived a framework for comprehending expected utility. At that point, it was considered the first and most thorough foundation to understanding the concept. Savage's framework involved proving that expected utility could be used to make an optimal choice among several acts through seven axioms. In his book, The Foundations of Statistics, Savage integrated a normative account of decision making under risk (when probabilities are known) and under uncertainty (when probabilities are not objectively known). Savage concluded that people have neutral attitudes towards uncertainty and that observation is enough to predict the probabilities of uncertain events. A crucial methodological aspect of Savage's framework is its focus on observable choices. Cognitive processes and other psychological aspects of decision making matter only to the extent that they have directly measurable implications on choice.
283:. For example, as someone gets wealthier, an extra dollar or an additional good is perceived as less valuable. In other words, desirability related with a financial gain depends not only on the gain itself but also on the wealth of the person. Bernoulli suggested that people maximize "moral expectation" rather than expected monetary value. Bernoulli made a clear distinction between expected value and expected utility. Instead of using the weighted outcomes, he used the weighted utility multiplied by probabilities. He proved that the utility function used in real life is finite, even when its expected value is infinite.
300:
we can anticipate what choices they are going to take. In this model, he defined numerical utilities for each option to exploit the richness of the space of prices. The outcome of each preference is exclusive of each other. For example, if you study, then you can not see your friends, however you will get a good grade in your course. In this scenario, we analyze personal preferences and beliefs and will be able to predict which option a person might choose (e.g. if someone prioritizes their social life over academic results, they will go out with their friends). Assuming that the decisions of a person are
3614:, subjects tend to value "p bets" (lotteries with a high chance of winning a low prize) lower than "$ bets" (lotteries with a small chance of winning a large prize). When subjects are asked which lotteries they prefer in direct comparison, however, they frequently prefer the "p bets" over "$ bets". Many studies have examined this "preference reversal", from both an experimental (e.g., Plott & Grether, 1979) and theoretical (e.g., Holt, 1986) standpoint, indicating that this behavior can be brought into accordance with neoclassical economic theory under specific assumptions.
432:
researchers to be "the most brilliant axiomatic theory of utility ever developed". Instead of assuming the probability of an event, Savage defines it in terms of preferences over acts. Savage used the states (something a person doesn't control) to calculate the probability of an event. On the other hand, he used utility and intrinsic preferences to predict the outcome of the event. Savage assumed that each act and state are sufficient to uniquely determine an outcome. However, this assumption breaks in cases where an individual does not have enough information about the event.
1529:
linear combination of the utilities of the outcomes, with the weights being the respective probabilities. Utility functions are also normally continuous functions. Such utility functions are also referred to as von
NeumannâMorgenstern (vNM) utility functions. This is a central theme of the expected utility hypothesis in which an individual chooses not the highest expected value, but rather the highest expected utility. The expected utility maximizing individual makes decisions rationally based on the axioms of the theory.
3035:
259:, which has broad application in economics in addition to expected utility theory. He used this concept to formalize the idea that the same amount of additional money was less useful to an already-wealthy person than it would be to a poor person. The theory can also more accurately describe more realistic scenarios (where expected values are finite) than expected value alone. He proposed that a nonlinear function of utility of an outcome should be used instead of the
3478:, expected utility theory is a simplification of reality. The mathematical correctness of expected utility theory and the salience of its primitive concepts do not guarantee that expected utility theory is a reliable guide to human behavior or optimal practice. The mathematical clarity of expected utility theory has helped scientists design experiments to test its adequacy, and to distinguish systematic departures from its predictions. This has led to the field of
5821:
5810:
2664:
3448:, other desirable ends can also be included in utility such as pleasure, knowledge, friendship, etc. Originally the total utility of the consumer was the sum of independent utilities of the goods. However, the expected value theory was dropped as it was considered too static and deterministic. The classical counter example to the expected value theory (where everyone makes the same "correct" choice) is the
3030:{\displaystyle {\begin{aligned}\operatorname {E} &=\operatorname {E} -b\operatorname {E} \\&=\operatorname {E} -b\operatorname {E} -a(w-\operatorname {E} )}]\\&=\operatorname {E} -be^{-a\operatorname {E} }\operatorname {E} )}]\\&={\text{expected wealth}}-b\cdot e^{-a\cdot {\text{expected wealth}}}\cdot {\text{risk}}.\end{aligned}}}
3547:
contexts are significantly different. This is demonstrated in the contrast of individual preferences under the insurance and lottery context shows the degree of indeterminacy of the expected utility theory. Additionally, experiments have shown systematic violations and generalizations based on the results of Savage and von
NeumannâMorgenstern.
436:
statement will be different for each person depending on intrinsic factors such as financial necessity or judgment about the company. For that reason, no state can rule out the performance of an act. Only when the state and the act are evaluated simultaneously, it becomes possible to determine an outcome with certainty.
435:
Additionally, he believed that outcomes must have the same utility regardless of state. For that reason, it is essential to correctly identify which statement is considered an outcome. For example, if someone says "I got the job" this affirmation is not considered an outcome, since the utility of the
3514:
According to the empirical results there has been almost no recognition in decision theory of the distinction between the problem of justifying its theoretical claims regarding the properties of rational belief and desire. One of the main reasons is because people's basic tastes and preferences for
3168:
is directly related to the curvature of the utility function: risk neutral individuals have linear utility functions, while risk seeking individuals have convex utility functions and risk averse individuals have concave utility functions. The degree of risk aversion can be measured by the curvature
1528:
In other words, if an individual's behavior always satisfies the above axioms, then there is a utility function such that the individual will choose one gamble over another if and only if the expected utility of one exceeds that of the other. The expected utility of any gamble may be expressed as a
299:
are defined over a set of bets where each option has a different yield. Ramsey believed that we always choose decisions to receive the best expected outcome according to our personal preferences. This implies that if we are able to understand the priorities and personal preferences of an individual
1664:
exhibits constant absolute risk aversion, and for this reason is often avoided, although it has the advantage of offering substantial mathematical tractability when asset returns are normally distributed. Note that, as per the affine transformation property alluded to above, the utility function
431:
The theory of subjective expected utility combines two concepts: first, a personal utility function, and second, a personal probability distribution (usually based on
Bayesian probability theory). This theoretical model has been known for its clear and elegant structure and its considered by some
3546:
are considered insufficient to predict preferences and the expected utility. Additionally, experiments have shown systematic violations and generalizations based on the results of Savage and von
NeumannâMorgenstern. This is because preferences and utility functions constructed under different
3410:
A decision that maximizes expected utility also maximizes the probability of the decision's consequences being preferable to some uncertain threshold. In the absence of uncertainty about the threshold, expected utility maximization simplifies to maximizing the probability of achieving some fixed
271:
is higher for low-probability events than the difference between the payout level of a particular outcome and its expected value. Bernoulli further proposed that it was not the goal of the gambler to maximize his expected gain but to instead maximize the logarithm of his gain.
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where it was demonstrated that people do not revise their degrees on belief in line with experimented probabilities and also that probabilities cannot be applied to single cases. On the other hand, in updating probability distributions using evidence, a standard method uses
1500:
If all these axioms are satisfied, then the individual is said to be rational and the preferences can be represented by a utility function, i.e. one can assign numbers (utilities) to each outcome of the lottery such that choosing the best lottery according to the preference
61:
The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e. the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities). The summarised formula for expected utility is
927:
pertains to well-defined preferences as well. It assumes that two gambles mixed with an irrelevant third one will maintain the same order of preference as when the two are presented independently of the third one. The independence axiom is the most controversial axiom..
218:
Although the expected utility hypothesis is standard in economic modelling, it has been found to be violated in psychological experiments. For many years, psychologists and economic theorists have been developing new theories to explain these deficiencies. These include
496:*If and only if all the axioms are satisfied one can use the information to reduce the uncertainty about the events that are out of their control. Additionally the theorem ranks the outcome according to a utility function that reflects the personal preferences.
3411:
target. If the uncertainty is uniformly distributed, then expected utility maximization becomes expected value maximization. Intermediate cases lead to increasing risk aversion above some fixed threshold and increasing risk seeking below a fixed threshold.
2587:, or in the unlikely case in which the utility function has a quadratic form. However, David E. Bell proposed a measure of risk which follows naturally from a certain class of von NeumannâMorgenstern utility functions. Let utility of wealth be given by
3141:
For general utility functions, however, expected utility analysis does not permit the expression of preferences to be separated into two parameters with one representing the expected value of the variable in question and the other representing its risk.
3592:
approaches to probability treat it as a degree of belief and thus they do not draw a distinction between risk and a wider concept of uncertainty: they deny the existence of
Knightian uncertainty. They would model uncertain probabilities with
3485:
Other critics argue applying expected utility to economic and policy decisions, has engendered inappropriate valuations, particularly in scenarios in which monetary units are used to scale the utility of nonmonetary outcomes, such as deaths.
3609:
Starting with studies such as
Lichtenstein & Slovic (1971), it was discovered that subjects sometimes exhibit signs of preference reversals with regard to their certainty equivalents of different lotteries. Specifically, when eliciting
3439:
In the early days of the calculus of probability, classic utilitarians believed that the option which has the greatest utility will produce more pleasure or happiness for the agent and therefore must be chosen. The main problem with the
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3394:
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In empirical applications, a number of violations of expected utility theory have been shown to be systematic and these falsifications have deepened understanding of how people actually decide.
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and its expected value are always negative: what matters for preference ordering is which of two gambles gives the higher expected utility, not the numerical values of those expected utilities.
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in which case the right side of this equation has a finite number of terms; or there could be an infinite set of discrete values, in which case the right side has an infinite number of terms.
3184:
is not an adequate measure of the risk aversion of a utility function. Instead, it needs to be normalized. This leads to the definition of the ArrowâPratt measure of absolute risk aversion:
304:, according to this theorem, we should be able to know the beliefs and utilities from a person just by looking at the choices they make (which is wrong). Ramsey defines a proposition as "
3444:
is that there might not be a unique correct way to quantify utility or to identify the best trade-offs. For example, some of the trade-offs may be intangible or qualitative. Rather than
1059:
1607:
was originally suggested by
Bernoulli (see above). It has relative risk aversion constant and equal to one, and is still sometimes assumed in economic analyses. The utility function
414:
124:
4480:
Subjects changed their beliefs faster by conditioning on evidence (Bayes's theorem) than by using informal reasoning, according to a classic study by the psychologist Ward
Edwards:
255:(involving infinite expected values) in 1713, prompting two Swiss mathematicians to develop expected utility theory as a solution. Bernoulli's paper was the first formalization of
1392:
448:(Savage, 1954) A preference < satisfies P1âP7 if and only if there is a finitely additive probability measure P and a function u : C â R such that for every pair of acts
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allowing different people to disagree about the degree of risk associated with any given portfolio. Individuals sharing a given risk measure (based on given value of
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illustrates that decision making based on expected value of monetary payoffs lead to absurd conclusions. When a probability distribution function has an infinite
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There are three components in the psychology field that are seen as crucial to the development of a more accurate descriptive theory of decision under risks.
3160:, meaning that the individual would refuse a fair gamble (a fair gamble has an expected value of zero). Risk aversion implies that their utility functions are
3494:
Psychologists have discovered systematic violations of probability calculations and behavior by humans. This have been evidenced with examples such as the
308:" when two possible outcomes have an equal value. In other words, if the probability can be defined in terms of a preference, each proposition should have
3894:
3534:" because they can depend on the way the problem is presented, not on the actual costs, rewards, or probabilities involved. Particular theories include
2142:
3530:
theories to account for instances where people's choices deviate from those predicted by expected utility theory. These deviations are described as "
3989:
Lindley DV (September 1973). "The foundations of statistics (second edition), by
Leonard J. Savage. Pp xv, 310. £1·75. 1972 (Dover/Constable)".
2412:
3597:, i.e. where the uncertain probabilities are modelled as distributions whose parameters are themselves drawn from a higher-level distribution (
3747:
518:
A consequence is the description of all that is relevant to the decision maker's utility (e.g. monetary rewards, psychological factors, etc)
4836:(1964). "Foresight: its Logical Laws, Its Subjective Sources (translation of the 1937 article in French". In Kyburg HE, Smokler HE (eds.).
4806:(September 1989). "Probabilism: A Critical Essay on the Theory of Probability and on the Value of Science (translation of 1931 article)".
1522:
547:
536:
506:
The specification of every aspect of the decision problem at hand or "A description of the world leaving no relevant aspect undescribed."
5956:
3772:
3043:
5857:
5691:
4972:
5190:
4191:
Owen J, Rabinovitch R (1983). "On the class of elliptical distributions and their applications to the theory of portfolio choice".
3309:
3190:
3562:
may occur. Thus one must make assumptions about the probabilities, but then the expected values of various decisions can be very
923:
204:
expresses the utility of each respective payoff. Graphically the curvature of the u function captures the agent's risk attitude.
4881:
4780:
4747:
4528:
4049:
3843:
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1779:
The class of constant relative risk aversion utility functions contains three categories. Bernoulli's utility function
3916:
790:
assumes that, as an individual decides according to the completeness axiom, the individual also decides consistently.
3566:
to the assumptions. This is particularly a problem when the expectation is dominated by rare extreme events, as in a
3511:
has suggested that humans change their beliefs faster when using
Bayesian methods than when using informal judgment.
2133:
3467:
which showed empirically, how preferences of individuals are inconsistent among the same choices, depending on the
17:
3707:
3539:
3404:
3400:
987:
224:
3574:
to uncertainty of probability of outcomes, either not depending on probabilities of outcomes and only requiring
1548:
is cardinal, in that implied behavior would be altered by a non-linear monotonic transformation of utility, the
6027:
295:
introduced the Ramsey's Representation Theorem. This representation theorem for expected utility assumed that
330:
5850:
5007:
65:
4164:
Chamberlain G (1983). "A characterization of the distributions that imply mean-variance utility functions".
562:
assumes that an individual has well defined preferences and can always decide between any two alternatives.
5382:
5183:
4635:
Lichtenstein S, Slovic P (1971). "Reversals of preference between bids and choices in gambling decisions".
4268:
3672:
3527:
2538:
292:
280:
211:
preferences. The expected utility hypothesis imposes limitations on the utility function and makes utility
3550:
In practice there will be many situations where the probabilities are unknown, and one is operating under
5676:
5316:
4857:
3722:
3627:
1365:
557:
4515:
Phillips LD, Edwards W (October 2008). "Chapter 6: Conservatism in a simple probability inference task (
1921:
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is ordinal because any monotonic increasing transformation of expected utility gives the same behavior.
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5996:
5971:
5338:
5326:
5321:
5311:
3727:
3543:
1968:
228:
4994:
Schoemaker PJ (1982). "The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations".
1883:
1838:
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5931:
5756:
5281:
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5023:
3468:
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2042:
554:
decision maker: completeness; transitivity; independence of irrelevant alternatives; and continuity.
3937:
2074:
6017:
5843:
5422:
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4703:
4674:
3567:
2571:
Often people refer to "risk" in the sense of a potentially quantifiable entity. In the context of
1613:
275:
Daniel Bernoulli drew attention to psychological and behavioral components behind the individual's
5104:
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
2016:
1785:
1563:
5991:
5824:
5721:
5716:
5666:
5539:
5417:
5176:
4672:
Grether DM, Plott CR (1979). "Economic Theory of Choice and the Preference Reversal Phenomenon".
3500:
3482:, which has produced deviations from expected utility theory to account for the empirical facts.
2584:
2572:
305:
276:
5060:
Briggs RA (2019). "Normative Theories of Rational Choice: Expected Utility". In Zalta EN (ed.).
4939:
961:
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635:
609:
5986:
5951:
5901:
5741:
5701:
5696:
5478:
5449:
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5228:
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Schoemaker PJ (1980). "Experiments on Decisions under Risk: The Expected Utility Hypothesis.".
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252:
51:
35:
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amounts to choosing the lottery with the highest expected utility. This result is called the
425:
3407:) functions, where ARA(w) is constant. They are often used in economics for simplification.
2356:
6022:
5981:
5885:
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5656:
5588:
5503:
5397:
5333:
5121:
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3657:
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is used as a risk measure for portfolio return; however, this is only valid if returns are
2329:
2262:
2108:
1461:
1084:
248:
176:
129:
4485:
Edwards W (1968). "Conservatism in Human Information Processing". In Kleinmuntz, B (ed.).
2511:
8:
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4255:
Aspects of the Theory of Risk Bearing Reprinted in Essays in the Theory of Risk Bearing
4208:
4146:
4014:
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3803:
3697:
3677:
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3559:
3523:
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3479:
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3283:
3103:, which differs between two individuals if they have different values of the parameter
2389:
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1397:
1345:
1295:
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1255:
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1215:
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685:
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156:
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5782:
5761:
5731:
5593:
5517:
5473:
5147:
5090:
4947:
Pfanzagl J, Baumann V, Huber H (1968). "Events, Utility and Subjective Probability".
4916:
4877:
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4776:
4769:
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4177:
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4092:
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4006:
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3839:
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3424:
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4959:(1993). "Chapter 7 (specifically) and 8, 9, 10, (to show paradoxes to the theory)".
4457:
4355:
3807:
3515:
losses cannot be represented with utility as they change under different scenarios.
5946:
5911:
5746:
5726:
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3967:
3963:
3875:
3831:
3787:
3692:
3594:
3161:
1541:
256:
4388:
Oberhelman DD (June 2001). Zalta EN (ed.). "Stanford Encyclopedia of Philosophy".
3791:
2406:
can take on any of a continuous range of values, the expected utility is given by
2249:{\displaystyle \operatorname {E} =p_{1}\cdot u(x_{1})+p_{2}\cdot u(x_{2})+\cdots }
5906:
5866:
5814:
5286:
5223:
4968:
4495:
4494:
Edwards W (1982). "Conservatism in Human Information Processing (excerpted)". In
3702:
3667:
3571:
3535:
3508:
3504:
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1537:
220:
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208:
39:
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5789:
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5488:
5407:
5199:
5044:
5011:
4895:
4401:
4339:
4226:
Bell DE (December 1988). "One-switch utility functions and a measure of risk".
3647:
3583:
3441:
3428:
260:
55:
47:
4739:
4282:
Pratt JW (JanuaryâApril 1964). "Risk aversion in the small and in the large".
4002:
3835:
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6011:
5711:
5611:
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4347:
4316:
Castagnoli and LiCalzi, 1996; Bordley and LiCalzi, 2000; Bordley and Kirkwood
4096:
4010:
3975:
3799:
3712:
3682:
3165:
3157:
3151:
1292:
in which the individual is then indifferent between this mix and the lottery
264:
4239:
4041:
3130:) may choose different portfolios because they may have different values of
5681:
5513:
5508:
5242:
5151:
5133:
4621:
4503:
3460:
1532:
The von NeumannâMorgenstern formulation is important in the application of
268:
4790:
Arrow KJ (1963). "Uncertainty and the Welfare Economics of Medical Care".
2498:{\displaystyle \operatorname {E} =\int _{-\infty }^{\infty }u(x)f(x)\,dx,}
2353:
is its probability. There could be either a finite set of possible values
2259:
where the left side is the subjective valuation of the gamble as a whole,
5976:
5706:
5618:
5498:
5350:
5264:
4956:
4499:
4129:
Borch K (January 1969). "A note on uncertainty and indifference curves".
3551:
2136:, the formula for expected utility, which is assumed to be maximized, is
301:
43:
1555:
50:
maximize utility, meaning the subjective desirability of their actions.
5466:
5218:
4716:
4687:
4443:
4303:
4212:
4150:
4087:
4070:
3598:
3156:
The expected utility theory takes into account that individuals may be
1533:
296:
4657:
2077:
of utility functions having hyperbolic absolute risk aversion (HARA).
419:
286:
5777:
5544:
5461:
5456:
5269:
4648:
3445:
1536:
to economics because it was developed shortly after the HicksâAllen "
4822:(1937). "La Prévision: ses lois logiques, ses sources subjectives".
4732:
Experiments on Decisions under Risk: The Expected Utility Hypothesis
4435:
4295:
4253:
Arrow KJ (1965). "The theory of risk aversion". In Saatio YJ (ed.).
4204:
4142:
526:
An act is a finite-valued function that maps states to consequences.
5569:
5564:
5439:
5082:
2576:
324:
in order to be indifferent between both options. Ramsey shows that
5835:
5116:
4701:
Holt C (1986). "Preference Reversals and the Independence Axiom".
4586:"Rationality, the Bayesian standpoint, and the Monty-Hall problem"
4036:, Berlin, New York: Walter de Gruyter, pp. 1â36, 2009-01-21,
3633:
Better understanding of the psychologically relevant outcome space
5926:
5921:
5623:
5522:
5434:
5168:
3579:
3096:{\displaystyle \operatorname {E} (e^{-a(w-\operatorname {E} w)})}
2566:
5809:
5598:
4549:
Vind K (February 2000). "von Neumann Morgenstern preferences".
3604:
4934:
Essays in Mathematical Economics In Honor of Oskar Morgenstern
3954:
Savage LJ (March 1951). "The Theory of Statistical Decision".
58:, builds this postulate to model aggregate social behaviour.
5483:
5365:
5345:
4915:
Pfanzagl J (1967). "Subjective Probability Derived from the
4118:(Third ed.). Princeton, NJ: Princeton University Press.
3389:{\displaystyle {\mathit {RRA}}(w)=-{\frac {wu''(w)}{u'(w)}}}
3270:{\displaystyle {\mathit {ARA}}(w)=-{\frac {u''(w)}{u'(w)}},}
5936:
5640:
3771:
Conte, Anna; Hey, John D.; Moffatt, Peter G. (2011-05-01).
932:
Axiom (Independence of irrelevant alternatives): For every
530:
4326:
Aase KK (January 2001). "On the St. Petersburg Paradox".
3917:"Normative Theories of Rational Choice: Expected Utility"
3321:
3318:
3202:
3199:
4980:
The Foundations of Mathematics and other Logical Essays
4521:
A Science of Decision Making:The Legacy of Ward Edwards
1544:
in economic theory. However, while in this context the
4109:
3303:
The ArrowâPratt measure of relative risk aversion is:
1832:
has relative risk aversion equal to 1. The functions
1704:
gives exactly the same preferences orderings as does
1523:
von NeumannâMorgenstern utility representation theorem
4417:"Prospect Theory: An Analysis of Decision under Risk"
3403:) functions, where RRA(w) is constant, and the CARA (
3312:
3286:
3193:
3109:
3046:
2667:
2596:
2547:
2514:
2415:
2392:
2359:
2332:
2296:
2265:
2145:
2111:
2091:
2045:
2019:
1971:
1924:
1886:
1841:
1788:
1746:
1710:
1671:
1616:
1566:
1556:
Examples of von NeumannâMorgenstern utility functions
1540:
revolution" of the 1930s, and it revived the idea of
1507:
1464:
1420:
1400:
1368:
1348:
1322:
1298:
1278:
1258:
1238:
1218:
1198:
1178:
1158:
1132:
1087:
1067:
990:
964:
938:
898:
872:
846:
826:
800:
768:
748:
728:
708:
688:
668:
638:
612:
592:
572:
541:
333:
179:
159:
132:
68:
5006:
4946:
4519:(1966) 72: 346-354)". In Weiss JW, Weiss DJ (eds.).
2132:
affects a person's utility takes on one of a set of
4257:. Chicago, 1971: Markham Publ. Co. pp. 90â109.
3636:
A psychologically richer theory of the determinants
3489:
3399:
Special classes of utility functions are the CRRA (
420:
Savage's subjective expected utility representation
287:
Ramsey-theoretic approach to subjective probability
5100:"The time resolution of the St Petersburg paradox"
4931:
4768:
4634:
4111:
3828:Expected Utility Hypotheses and the Allais Paradox
3388:
3292:
3269:
3164:and show diminishing marginal wealth utility. The
3118:
3095:
3029:
2639:
2556:
2529:
2497:
2398:
2375:
2345:
2318:
2278:
2248:
2124:
2097:
2063:
2031:
2002:
1954:
1910:
1869:
1821:
1768:
1732:
1696:
1653:
1599:
1513:
1488:
1450:
1406:
1386:
1354:
1334:
1304:
1284:
1264:
1244:
1224:
1204:
1184:
1164:
1144:
1111:
1073:
1053:
976:
950:
910:
884:
858:
832:
812:
774:
754:
734:
714:
694:
674:
650:
624:
598:
578:
439:
408:
215:(though still not comparable across individuals).
192:
165:
145:
118:
5031:Aase KK (2001). "On the St. Petersburg Paradox".
4508:Judgment under uncertainty: Heuristics and biases
4071:"Attitudes to Uncertainty in a Strategic Setting"
1252:, then there should be a possible combination of
6009:
4068:
4874:Selected Economic Writings of Oskar Morgenstern
4514:
4414:
4190:
3956:Journal of the American Statistical Association
3770:
2080:
4961:The psychology of judgment and decision making
4842:. Vol. 7. New York: Wiley. pp. 1â68.
3895:"Ramsey and the Ethically Neutral Proposition"
2567:Measuring risk in the expected utility context
279:and proposed that the utility of wealth has a
5851:
5184:
4890:
4876:. New York University Press. pp. 65â70.
3949:
3947:
3471:of the choices, i.e. how they are presented.
3414:
3172:Since the risk attitudes are unchanged under
1126:assumes that when there are three lotteries (
550:of the expected utility theory that define a
4671:
3748:"Expected Utility Theory | Encyclopedia.com"
3605:Preference reversals over uncertain outcomes
2650:for individual-specific positive parameters
499:The key ingredients in Savage's theory are:
4904:Memoirs of the National Academy of Sciences
4864:
4163:
3825:
3586:), or being less sensitive to assumptions.
1740:; thus it is irrelevant that the values of
1054:{\displaystyle tA+(1-t)C\succeq tB+(1-t)C,}
153:is the probability that outcome indexed by
5957:Heuristics in judgment and decision-making
5858:
5844:
5191:
5177:
5158:
5069:Hacking I (1980). "Strange Expectations".
4993:
4848:
4832:
4818:
4802:
4729:
4387:
4064:
4062:
4060:
3944:
243:
5141:
5115:
5020:Decision-Making: An Experimental Approach
4771:Foundations of Rational Choice Under Risk
4656:
4611:
4601:
4086:
4069:Li Z, Loomes G, Pogrebna G (2017-05-01).
2485:
4914:
4583:
4523:. Oxford University Press. p. 536.
4032:"1. Foundations of probability theory",
3518:
409:{\displaystyle P(E)=(1-U(m))(U(b)-U(w))}
5068:
5062:The Stanford Encyclopedia of Philosophy
4938:. Princeton University Press. pp.
4493:
4487:Formal Representation of Human Judgment
4484:
4057:
3988:
3858:
924:Independence of irrelevant alternatives
662:This means that the individual prefers
537:Von NeumannâMorgenstern utility theorem
531:Von NeumannâMorgenstern utility theorem
119:{\displaystyle U(p)=\sum u(x_{k})p_{k}}
14:
6010:
5097:
5059:
4967:
4368:
4110:von Neumann J, Morgenstern O (1953) .
3953:
3914:
3570:. Alternative decision techniques are
5839:
5172:
4955:
4789:
4766:
4544:
4542:
4281:
4252:
4128:
4114:Theory of Games and Economic Behavior
3773:"Mixture models of choice under risk"
2658:. Then expected utility is given by
2039:have relative risk aversion equal to
1918:have relative risk aversion equal to
512:A set of states identified by someone
207:Standard utility functions represent
5030:
4973:"Chapter VII: Truth and Probability"
4824:Annales de l'Institut Henri Poincaré
4700:
4548:
4458:"Expected utility | decision theory"
4325:
4225:
3821:
3819:
3817:
5865:
5161:Experiments on Decisions under Risk
4900:"On Small Differences in Sensation"
4775:. Oxford: Oxford University Press.
4375:Stanford Encyclopedia of Philosophy
3892:
3830:. Dordrecht: Springer Netherlands.
1387:{\displaystyle A\succeq B\succeq C}
24:
5747:Microfoundations of macroeconomics
5198:
4759:
4723:
4637:Journal of Experimental Psychology
4539:
4517:Journal of Experimental Psychology
4381:
4319:
4275:
4246:
3880:10.1111/j.1746-8361.2004.tb00320.x
3617:
3315:
3196:
3076:
3047:
2944:
2915:
2898:
2866:
2833:
2803:
2783:
2762:
2724:
2703:
2672:
2456:
2451:
2416:
2146:
1955:{\displaystyle 1-\alpha \in (0,1)}
542:The von NeumannâMorgenstern axioms
25:
6049:
4839:Studies in Subjective Probability
4551:Journal of Mathematical Economics
3861:"Ramsey's Representation Theorem"
3814:
2003:{\displaystyle u(w)=-w^{\alpha }}
5820:
5819:
5808:
3826:Allais M, Hagen O, eds. (1979).
3490:Conservatism in updating beliefs
3145:
2585:jointly elliptically distributed
1911:{\displaystyle \alpha \in (0,1)}
1870:{\displaystyle u(w)=w^{\alpha }}
794:Axiom (Transitivity): For every
566:Axiom (Completeness): For every
238:
34:is a foundational assumption in
4694:
4665:
4628:
4577:
4474:
4450:
4408:
4369:Martin, Robert (16 June 2008).
4362:
4310:
4219:
4184:
4157:
4122:
4103:
3708:Rank-dependent expected utility
3540:rank-dependent expected utility
3405:constant absolute risk aversion
3401:constant relative risk aversion
2640:{\displaystyle u(w)=w-be^{-aw}}
2064:{\displaystyle 1-\alpha >1.}
440:Savage's representation theorem
225:rank-dependent expected utility
5033:Scandinavian Actuarial Journal
4996:Journal of Economic Literature
4415:Kahneman D, Tversky A (1979).
4328:Scandinavian Actuarial Journal
4034:Interpretations of Probability
4025:
3982:
3968:10.1080/01621459.1951.10500768
3908:
3902:Australian National University
3886:
3852:
3764:
3740:
3380:
3374:
3361:
3355:
3332:
3326:
3258:
3252:
3239:
3233:
3213:
3207:
3090:
3085:
3067:
3053:
2964:
2959:
2956:
2950:
2935:
2921:
2910:
2904:
2878:
2872:
2853:
2848:
2845:
2839:
2824:
2815:
2809:
2789:
2774:
2768:
2749:
2730:
2715:
2709:
2693:
2690:
2684:
2678:
2606:
2600:
2524:
2518:
2482:
2476:
2470:
2464:
2437:
2434:
2428:
2422:
2313:
2300:
2237:
2224:
2202:
2189:
2167:
2164:
2158:
2152:
1981:
1975:
1949:
1937:
1905:
1893:
1851:
1845:
1816:
1810:
1798:
1792:
1626:
1620:
1594:
1588:
1576:
1570:
1483:
1471:
1442:
1430:
1106:
1094:
1042:
1030:
1012:
1000:
403:
400:
394:
385:
379:
373:
370:
367:
361:
349:
343:
337:
263:of an outcome, accounting for
103:
90:
78:
72:
13:
1:
4872:". In Andrew Schotter (ed.).
4868:(1976). "Some Reflections on
4563:10.1016/s0304-4068(99)00004-x
4510:. Cambridge University Press.
3792:10.1016/j.jeconom.2009.10.011
3734:
1654:{\displaystyle u(w)=-e^{-aw}}
1172:) and the individual prefers
446:Savage representation theorem
4371:"The St. Petersburg Paradox"
4178:10.1016/0022-0531(83)90129-1
3673:Generalized expected utility
3528:generalized expected utility
3434:
2539:probability density function
2081:Formula for expected utility
2032:{\displaystyle \alpha <0}
1822:{\displaystyle u(w)=\log(w)}
1600:{\displaystyle u(w)=\log(w)}
1061:must hold for every lottery
742:, or is indifferent between
281:diminishing marginal utility
7:
5881:Expected utility hypothesis
5692:Civil engineering economics
5677:Statistical decision theory
5317:Income elasticity of demand
3723:Subjective expected utility
3640:
32:expected utility hypothesis
10:
6054:
5997:Evidential decision theory
5327:Price elasticity of supply
5322:Price elasticity of demand
5312:Cross elasticity of demand
5045:10.1080/034612301750077356
4951:. Wiley. pp. 195â220.
4402:10.1108/rr.2001.15.6.9.311
4340:10.1080/034612301750077356
4166:Journal of Economic Theory
4131:Review of Economic Studies
3728:Two-moment decision models
3544:cumulative prospect theory
3415:The St. Petersburg paradox
3149:
977:{\displaystyle A\succeq B}
911:{\displaystyle A\succeq C}
885:{\displaystyle B\succeq C}
859:{\displaystyle A\succeq B}
651:{\displaystyle A\preceq B}
625:{\displaystyle A\succeq B}
534:
229:cumulative prospect theory
200:is realized, and function
5932:Principle of indifference
5894:
5873:
5803:
5770:
5649:
5206:
5024:Stanford University Press
4740:10.1007/978-94-017-5040-0
4584:Baratgin J (2015-08-11).
4003:10.1017/s0025557200132589
3836:10.1007/978-94-015-7629-1
3169:of the utility function.
3040:Thus the risk measure is
1697:{\displaystyle K-e^{-aw}}
1550:expected utility function
1451:{\displaystyle pA+(1-p)C}
5383:Incomeâconsumption curve
4792:American Economic Review
4704:American Economic Review
4675:American Economic Review
4603:10.3389/fpsyg.2015.01168
4267:: CS1 maint: location (
3991:The Mathematical Gazette
3915:Briggs RA (2014-08-08).
3568:long-tailed distribution
3463:in 1979 presented their
3180:, the second derivative
2319:{\displaystyle u(x_{i})}
1769:{\displaystyle -e^{-aw}}
1733:{\displaystyle -e^{-aw}}
1514:{\displaystyle \succeq }
1414:is equally preferred to
1316:Axiom (Continuity): Let
5992:Emotional choice theory
5717:Industrial organization
4590:Frontiers in Psychology
4462:Encyclopedia Britannica
4240:10.1287/mnsc.34.12.1416
4042:10.1515/9783110213195.1
3780:Journal of Econometrics
3501:conditional probability
277:decision-making process
244:Bernoulli's formulation
5987:Causal decision theory
5952:St. Petersburg paradox
5902:Decision-matrix method
5134:10.1098/rsta.2011.0065
4730:Schoemaker PJ (1980).
3932:Cite journal requires
3450:St. Petersburg Paradox
3421:St. Petersburg paradox
3390:
3294:
3271:
3174:affine transformations
3120:
3097:
3031:
2641:
2573:mean-variance analysis
2558:
2531:
2499:
2400:
2377:
2376:{\displaystyle x_{i},}
2347:
2326:is its valuation, and
2320:
2280:
2250:
2126:
2099:
2065:
2033:
2004:
1956:
1912:
1871:
1823:
1770:
1734:
1698:
1655:
1601:
1515:
1490:
1452:
1408:
1388:
1356:
1336:
1306:
1286:
1266:
1246:
1226:
1206:
1186:
1166:
1146:
1113:
1075:
1055:
978:
952:
912:
886:
860:
834:
814:
776:
756:
736:
716:
696:
676:
652:
626:
600:
580:
410:
253:St. Petersburg paradox
194:
167:
147:
120:
52:Rational choice theory
36:mathematical economics
6028:Motivational theories
5967:Bayesian epistemology
5687:Engineering economics
5282:Costâbenefit analysis
5071:Philosophy of Science
4949:Theory of Measurement
4854:Theory of Probability
3688:Lottery (probability)
3612:certainty equivalents
3556:Knightian uncertainty
3526:has produced several
3519:Irrational deviations
3442:expected value theory
3391:
3295:
3272:
3136:Entropic risk measure
3121:
3098:
3032:
2642:
2559:
2532:
2500:
2401:
2378:
2348:
2346:{\displaystyle p_{i}}
2321:
2290:th possible outcome,
2281:
2279:{\displaystyle x_{i}}
2251:
2127:
2125:{\displaystyle x_{i}}
2100:
2066:
2034:
2005:
1962:. And the functions
1957:
1913:
1872:
1824:
1771:
1735:
1699:
1656:
1602:
1560:The utility function
1516:
1491:
1489:{\displaystyle p\in }
1453:
1409:
1389:
1357:
1337:
1307:
1287:
1267:
1247:
1227:
1207:
1187:
1167:
1147:
1114:
1112:{\displaystyle t\in }
1076:
1056:
979:
953:
913:
887:
861:
835:
815:
777:
757:
737:
717:
697:
677:
653:
627:
601:
581:
426:Leonard Jimmie Savage
411:
195:
193:{\displaystyle x_{k}}
168:
148:
146:{\displaystyle p_{k}}
121:
46:. It postulates that
5982:Social choice theory
5886:Intertemporal choice
5504:Price discrimination
5398:Intertemporal choice
4075:The Economic Journal
3752:www.encyclopedia.com
3663:Behavioral economics
3658:Bayesian probability
3310:
3284:
3191:
3107:
3044:
2665:
2594:
2581:normally distributed
2545:
2530:{\displaystyle f(x)}
2512:
2413:
2390:
2357:
2330:
2294:
2263:
2143:
2109:
2089:
2043:
2017:
1969:
1922:
1884:
1839:
1786:
1744:
1708:
1669:
1614:
1564:
1505:
1462:
1418:
1398:
1366:
1346:
1320:
1296:
1276:
1256:
1236:
1216:
1196:
1176:
1156:
1130:
1085:
1065:
988:
962:
936:
896:
870:
844:
824:
798:
766:
746:
726:
706:
686:
666:
636:
610:
590:
570:
331:
177:
157:
130:
66:
27:Concept in economics
5917:Strategic dominance
5815:Business portal
5752:Operations research
5579:Substitution effect
5126:2011RSPTA.369.4913P
5110:(1956): 4913â4931.
3630:effect (psychology)
3595:hierarchical models
3507:. An experiment on
3446:monetary incentives
2460:
1335:{\displaystyle A,B}
1145:{\displaystyle A,B}
951:{\displaystyle A,B}
813:{\displaystyle A,B}
233:bounded rationality
54:, a cornerstone of
5962:Probability theory
5393:Indifference curve
5361:Goods and services
5302:Economies of scope
5297:Economies of scale
5098:Peters O (2011) .
4860:. New York: Wiley.
4228:Management Science
4193:Journal of Finance
4088:10.1111/ecoj.12486
3859:Bradley R (2004).
3718:Risk in psychology
3698:Priority heuristic
3678:Indifference price
3653:Ambiguity aversion
3524:Behavioral finance
3496:Monty Hall problem
3480:behavioral finance
3476:mathematical model
3386:
3290:
3267:
3119:{\displaystyle a,}
3116:
3093:
3027:
3025:
2637:
2557:{\displaystyle x.}
2554:
2527:
2495:
2443:
2396:
2373:
2343:
2316:
2276:
2246:
2122:
2095:
2061:
2029:
2000:
1952:
1908:
1867:
1819:
1766:
1730:
1694:
1651:
1597:
1511:
1486:
1448:
1404:
1384:
1362:be lotteries with
1352:
1332:
1302:
1282:
1262:
1242:
1222:
1202:
1182:
1162:
1142:
1109:
1071:
1051:
974:
948:
908:
882:
856:
830:
810:
772:
752:
732:
712:
692:
672:
648:
622:
596:
576:
406:
249:Nicolaus Bernoulli
190:
163:
143:
116:
6033:Optimal decisions
6005:
6004:
5833:
5832:
5795:Political economy
5594:Supply and demand
5474:Pareto efficiency
4883:978-0-8147-7771-8
4782:978-0-19-823303-9
4749:978-94-017-5042-4
4530:978-0-19-532298-9
4390:Reference Reviews
4051:978-3-11-021319-5
3845:978-90-481-8354-8
3576:scenario analysis
3425:Nicolas Bernoulli
3384:
3293:{\displaystyle w}
3262:
3018:
3008:
2980:
2399:{\displaystyle x}
2098:{\displaystyle x}
1407:{\displaystyle B}
1355:{\displaystyle C}
1305:{\displaystyle B}
1285:{\displaystyle C}
1265:{\displaystyle A}
1245:{\displaystyle C}
1225:{\displaystyle B}
1205:{\displaystyle B}
1185:{\displaystyle A}
1165:{\displaystyle C}
1074:{\displaystyle C}
984:, the preference
833:{\displaystyle C}
775:{\displaystyle B}
755:{\displaystyle A}
735:{\displaystyle A}
715:{\displaystyle B}
695:{\displaystyle B}
675:{\displaystyle A}
599:{\displaystyle B}
579:{\displaystyle A}
306:ethically neutral
166:{\displaystyle k}
16:(Redirected from
6045:
6038:Expected utility
5947:Ellsberg paradox
5912:Expected utility
5860:
5853:
5846:
5837:
5836:
5823:
5822:
5813:
5812:
5555:Returns to scale
5413:Market structure
5193:
5186:
5179:
5170:
5169:
5164:
5155:
5145:
5119:
5094:
5065:
5056:
5027:
5003:
4990:
4988:
4982:. Archived from
4977:
4964:
4952:
4943:
4937:
4911:
4887:
4861:
4856:. Translated by
4843:
4827:
4815:
4799:
4786:
4774:
4767:Anand P (1993).
4754:
4753:
4727:
4721:
4720:
4698:
4692:
4691:
4669:
4663:
4662:
4660:
4649:10.1037/h0031207
4632:
4626:
4625:
4615:
4605:
4581:
4575:
4574:
4546:
4537:
4534:
4511:
4490:
4478:
4472:
4471:
4469:
4468:
4454:
4448:
4447:
4421:
4412:
4406:
4405:
4385:
4379:
4378:
4366:
4360:
4359:
4323:
4317:
4314:
4308:
4307:
4290:(1/2): 122â136.
4279:
4273:
4272:
4266:
4258:
4250:
4244:
4243:
4223:
4217:
4216:
4188:
4182:
4181:
4161:
4155:
4154:
4126:
4120:
4119:
4117:
4107:
4101:
4100:
4090:
4081:(601): 809â826.
4066:
4055:
4054:
4029:
4023:
4022:
3997:(401): 220â221.
3986:
3980:
3979:
3951:
3942:
3941:
3935:
3930:
3928:
3920:
3912:
3906:
3905:
3899:
3890:
3884:
3883:
3865:
3856:
3850:
3849:
3823:
3812:
3811:
3777:
3768:
3762:
3761:
3759:
3758:
3744:
3693:Marginal utility
3628:decision framing
3554:. In economics,
3395:
3393:
3392:
3387:
3385:
3383:
3373:
3364:
3354:
3342:
3325:
3324:
3299:
3297:
3296:
3291:
3276:
3274:
3273:
3268:
3263:
3261:
3251:
3242:
3232:
3223:
3206:
3205:
3125:
3123:
3122:
3117:
3102:
3100:
3099:
3094:
3089:
3088:
3036:
3034:
3033:
3028:
3026:
3019:
3016:
3011:
3010:
3009:
3006:
2981:
2978:
2970:
2963:
2962:
2914:
2913:
2859:
2852:
2851:
2755:
2748:
2747:
2646:
2644:
2643:
2638:
2636:
2635:
2563:
2561:
2560:
2555:
2536:
2534:
2533:
2528:
2504:
2502:
2501:
2496:
2459:
2454:
2405:
2403:
2402:
2397:
2382:
2380:
2379:
2374:
2369:
2368:
2352:
2350:
2349:
2344:
2342:
2341:
2325:
2323:
2322:
2317:
2312:
2311:
2285:
2283:
2282:
2277:
2275:
2274:
2255:
2253:
2252:
2247:
2236:
2235:
2217:
2216:
2201:
2200:
2182:
2181:
2131:
2129:
2128:
2123:
2121:
2120:
2104:
2102:
2101:
2096:
2085:When the entity
2070:
2068:
2067:
2062:
2038:
2036:
2035:
2030:
2009:
2007:
2006:
2001:
1999:
1998:
1961:
1959:
1958:
1953:
1917:
1915:
1914:
1909:
1876:
1874:
1873:
1868:
1866:
1865:
1828:
1826:
1825:
1820:
1775:
1773:
1772:
1767:
1765:
1764:
1739:
1737:
1736:
1731:
1729:
1728:
1703:
1701:
1700:
1695:
1693:
1692:
1660:
1658:
1657:
1652:
1650:
1649:
1606:
1604:
1603:
1598:
1546:utility function
1542:cardinal utility
1520:
1518:
1517:
1512:
1495:
1493:
1492:
1487:
1457:
1455:
1454:
1449:
1413:
1411:
1410:
1405:
1393:
1391:
1390:
1385:
1361:
1359:
1358:
1353:
1341:
1339:
1338:
1333:
1311:
1309:
1308:
1303:
1291:
1289:
1288:
1283:
1271:
1269:
1268:
1263:
1251:
1249:
1248:
1243:
1231:
1229:
1228:
1223:
1211:
1209:
1208:
1203:
1191:
1189:
1188:
1183:
1171:
1169:
1168:
1163:
1151:
1149:
1148:
1143:
1118:
1116:
1115:
1110:
1080:
1078:
1077:
1072:
1060:
1058:
1057:
1052:
983:
981:
980:
975:
957:
955:
954:
949:
917:
915:
914:
909:
891:
889:
888:
883:
865:
863:
862:
857:
839:
837:
836:
831:
819:
817:
816:
811:
781:
779:
778:
773:
761:
759:
758:
753:
741:
739:
738:
733:
721:
719:
718:
713:
701:
699:
698:
693:
681:
679:
678:
673:
657:
655:
654:
649:
631:
629:
628:
623:
605:
603:
602:
597:
585:
583:
582:
577:
415:
413:
412:
407:
323:
321:
320:
317:
314:
257:marginal utility
199:
197:
196:
191:
189:
188:
172:
170:
169:
164:
152:
150:
149:
144:
142:
141:
125:
123:
122:
117:
115:
114:
102:
101:
21:
18:Expected utility
6053:
6052:
6048:
6047:
6046:
6044:
6043:
6042:
6018:Belief revision
6008:
6007:
6006:
6001:
5907:Decision matrix
5890:
5869:
5867:Decision theory
5864:
5834:
5829:
5807:
5799:
5766:
5645:
5287:Deadweight loss
5224:Consumer choice
5202:
5197:
5167:
4986:
4975:
4884:
4783:
4762:
4760:Further reading
4757:
4750:
4728:
4724:
4699:
4695:
4670:
4666:
4633:
4629:
4582:
4578:
4547:
4540:
4531:
4496:Daniel Kahneman
4481:
4479:
4475:
4466:
4464:
4456:
4455:
4451:
4436:10.2307/1914185
4419:
4413:
4409:
4386:
4382:
4367:
4363:
4324:
4320:
4315:
4311:
4296:10.2307/1913738
4280:
4276:
4260:
4259:
4251:
4247:
4234:(12): 1416â24.
4224:
4220:
4205:10.2307/2328079
4189:
4185:
4162:
4158:
4143:10.2307/2296336
4127:
4123:
4108:
4104:
4067:
4058:
4052:
4031:
4030:
4026:
3987:
3983:
3952:
3945:
3933:
3931:
3922:
3921:
3913:
3909:
3897:
3891:
3887:
3863:
3857:
3853:
3846:
3824:
3815:
3775:
3769:
3765:
3756:
3754:
3746:
3745:
3741:
3737:
3732:
3703:Prospect theory
3668:Decision theory
3643:
3620:
3618:Recommendations
3607:
3536:prospect theory
3521:
3509:belief revision
3492:
3465:prospect theory
3457:Daniel Kahneman
3437:
3417:
3366:
3365:
3347:
3343:
3341:
3314:
3313:
3311:
3308:
3307:
3285:
3282:
3281:
3244:
3243:
3225:
3224:
3222:
3195:
3194:
3192:
3189:
3188:
3154:
3148:
3108:
3105:
3104:
3060:
3056:
3045:
3042:
3041:
3024:
3023:
3015:
3007:expected wealth
3005:
2995:
2991:
2979:expected wealth
2977:
2968:
2967:
2928:
2924:
2891:
2887:
2857:
2856:
2796:
2792:
2753:
2752:
2737:
2733:
2696:
2668:
2666:
2663:
2662:
2625:
2621:
2595:
2592:
2591:
2569:
2546:
2543:
2542:
2513:
2510:
2509:
2455:
2447:
2414:
2411:
2410:
2391:
2388:
2387:
2364:
2360:
2358:
2355:
2354:
2337:
2333:
2331:
2328:
2327:
2307:
2303:
2295:
2292:
2291:
2270:
2266:
2264:
2261:
2260:
2231:
2227:
2212:
2208:
2196:
2192:
2177:
2173:
2144:
2141:
2140:
2134:discrete values
2116:
2112:
2110:
2107:
2106:
2090:
2087:
2086:
2083:
2044:
2041:
2040:
2018:
2015:
2014:
1994:
1990:
1970:
1967:
1966:
1923:
1920:
1919:
1885:
1882:
1881:
1861:
1857:
1840:
1837:
1836:
1787:
1784:
1783:
1754:
1750:
1745:
1742:
1741:
1718:
1714:
1709:
1706:
1705:
1682:
1678:
1670:
1667:
1666:
1639:
1635:
1615:
1612:
1611:
1565:
1562:
1561:
1558:
1506:
1503:
1502:
1463:
1460:
1459:
1419:
1416:
1415:
1399:
1396:
1395:
1367:
1364:
1363:
1347:
1344:
1343:
1321:
1318:
1317:
1297:
1294:
1293:
1277:
1274:
1273:
1257:
1254:
1253:
1237:
1234:
1233:
1217:
1214:
1213:
1197:
1194:
1193:
1177:
1174:
1173:
1157:
1154:
1153:
1131:
1128:
1127:
1086:
1083:
1082:
1066:
1063:
1062:
989:
986:
985:
963:
960:
959:
937:
934:
933:
897:
894:
893:
871:
868:
867:
845:
842:
841:
825:
822:
821:
799:
796:
795:
767:
764:
763:
747:
744:
743:
727:
724:
723:
707:
704:
703:
687:
684:
683:
667:
664:
663:
637:
634:
633:
611:
608:
607:
591:
588:
587:
571:
568:
567:
544:
539:
533:
442:
422:
332:
329:
328:
318:
315:
312:
311:
309:
289:
246:
241:
221:prospect theory
184:
180:
178:
175:
174:
158:
155:
154:
137:
133:
131:
128:
127:
110:
106:
97:
93:
67:
64:
63:
48:rational agents
40:decision making
28:
23:
22:
15:
12:
11:
5:
6051:
6041:
6040:
6035:
6030:
6025:
6020:
6003:
6002:
6000:
5999:
5994:
5989:
5984:
5979:
5974:
5969:
5964:
5959:
5954:
5949:
5944:
5942:Allais paradox
5939:
5934:
5929:
5924:
5919:
5914:
5909:
5904:
5898:
5896:
5892:
5891:
5889:
5888:
5883:
5877:
5875:
5871:
5870:
5863:
5862:
5855:
5848:
5840:
5831:
5830:
5828:
5827:
5817:
5804:
5801:
5800:
5798:
5797:
5792:
5790:Macroeconomics
5787:
5786:
5785:
5774:
5772:
5768:
5767:
5765:
5764:
5759:
5754:
5749:
5744:
5739:
5734:
5729:
5724:
5719:
5714:
5709:
5704:
5699:
5694:
5689:
5684:
5679:
5674:
5669:
5664:
5659:
5653:
5651:
5647:
5646:
5644:
5643:
5638:
5637:
5636:
5631:
5621:
5616:
5615:
5614:
5605:
5591:
5586:
5581:
5576:
5567:
5562:
5557:
5552:
5547:
5542:
5537:
5532:
5527:
5526:
5525:
5520:
5511:
5506:
5501:
5496:
5491:
5489:Price controls
5481:
5476:
5471:
5470:
5469:
5464:
5459:
5454:
5453:
5452:
5447:
5437:
5432:
5431:
5430:
5425:
5410:
5408:Market failure
5405:
5400:
5395:
5390:
5385:
5380:
5375:
5374:
5373:
5368:
5358:
5353:
5348:
5343:
5342:
5341:
5331:
5330:
5329:
5324:
5319:
5314:
5304:
5299:
5294:
5289:
5284:
5279:
5278:
5277:
5272:
5267:
5262:
5261:
5260:
5250:
5245:
5235:
5226:
5221:
5216:
5210:
5208:
5204:
5203:
5200:Microeconomics
5196:
5195:
5188:
5181:
5173:
5166:
5165:
5156:
5095:
5083:10.1086/288956
5077:(4): 562â567.
5066:
5057:
5028:
5004:
4991:
4989:on 2006-10-14.
4965:
4953:
4944:
4924:Utility Theory
4912:
4888:
4882:
4862:
4845:
4844:
4829:
4828:
4816:
4800:
4787:
4781:
4763:
4761:
4758:
4756:
4755:
4748:
4722:
4711:(3): 508â515.
4693:
4682:(4): 623â638.
4664:
4627:
4576:
4557:(1): 109â122.
4538:
4536:
4535:
4529:
4512:
4491:
4473:
4449:
4430:(2): 263â292.
4407:
4380:
4361:
4318:
4309:
4274:
4245:
4218:
4199:(3): 745â752.
4183:
4172:(1): 185â201.
4156:
4121:
4102:
4056:
4050:
4024:
3981:
3962:(253): 55â67.
3943:
3934:|journal=
3907:
3885:
3874:(4): 483â498.
3851:
3844:
3813:
3763:
3738:
3736:
3733:
3731:
3730:
3725:
3720:
3715:
3710:
3705:
3700:
3695:
3690:
3685:
3680:
3675:
3670:
3665:
3660:
3655:
3650:
3648:Allais paradox
3644:
3642:
3639:
3638:
3637:
3634:
3631:
3619:
3616:
3606:
3603:
3584:minimax regret
3520:
3517:
3491:
3488:
3436:
3433:
3429:expected value
3416:
3413:
3397:
3396:
3382:
3379:
3376:
3372:
3369:
3363:
3360:
3357:
3353:
3350:
3346:
3340:
3337:
3334:
3331:
3328:
3323:
3320:
3317:
3289:
3278:
3277:
3266:
3260:
3257:
3254:
3250:
3247:
3241:
3238:
3235:
3231:
3228:
3221:
3218:
3215:
3212:
3209:
3204:
3201:
3198:
3150:Main article:
3147:
3144:
3115:
3112:
3092:
3087:
3084:
3081:
3078:
3075:
3072:
3069:
3066:
3063:
3059:
3055:
3052:
3049:
3038:
3037:
3022:
3014:
3004:
3001:
2998:
2994:
2990:
2987:
2984:
2976:
2973:
2971:
2969:
2966:
2961:
2958:
2955:
2952:
2949:
2946:
2943:
2940:
2937:
2934:
2931:
2927:
2923:
2920:
2917:
2912:
2909:
2906:
2903:
2900:
2897:
2894:
2890:
2886:
2883:
2880:
2877:
2874:
2871:
2868:
2865:
2862:
2860:
2858:
2855:
2850:
2847:
2844:
2841:
2838:
2835:
2832:
2829:
2826:
2823:
2820:
2817:
2814:
2811:
2808:
2805:
2802:
2799:
2795:
2791:
2788:
2785:
2782:
2779:
2776:
2773:
2770:
2767:
2764:
2761:
2758:
2756:
2754:
2751:
2746:
2743:
2740:
2736:
2732:
2729:
2726:
2723:
2720:
2717:
2714:
2711:
2708:
2705:
2702:
2699:
2697:
2695:
2692:
2689:
2686:
2683:
2680:
2677:
2674:
2671:
2670:
2648:
2647:
2634:
2631:
2628:
2624:
2620:
2617:
2614:
2611:
2608:
2605:
2602:
2599:
2568:
2565:
2553:
2550:
2526:
2523:
2520:
2517:
2506:
2505:
2494:
2491:
2488:
2484:
2481:
2478:
2475:
2472:
2469:
2466:
2463:
2458:
2453:
2450:
2446:
2442:
2439:
2436:
2433:
2430:
2427:
2424:
2421:
2418:
2395:
2372:
2367:
2363:
2340:
2336:
2315:
2310:
2306:
2302:
2299:
2273:
2269:
2257:
2256:
2245:
2242:
2239:
2234:
2230:
2226:
2223:
2220:
2215:
2211:
2207:
2204:
2199:
2195:
2191:
2188:
2185:
2180:
2176:
2172:
2169:
2166:
2163:
2160:
2157:
2154:
2151:
2148:
2119:
2115:
2094:
2082:
2079:
2075:the discussion
2060:
2057:
2054:
2051:
2048:
2028:
2025:
2022:
2011:
2010:
1997:
1993:
1989:
1986:
1983:
1980:
1977:
1974:
1951:
1948:
1945:
1942:
1939:
1936:
1933:
1930:
1927:
1907:
1904:
1901:
1898:
1895:
1892:
1889:
1878:
1877:
1864:
1860:
1856:
1853:
1850:
1847:
1844:
1830:
1829:
1818:
1815:
1812:
1809:
1806:
1803:
1800:
1797:
1794:
1791:
1763:
1760:
1757:
1753:
1749:
1727:
1724:
1721:
1717:
1713:
1691:
1688:
1685:
1681:
1677:
1674:
1662:
1661:
1648:
1645:
1642:
1638:
1634:
1631:
1628:
1625:
1622:
1619:
1596:
1593:
1590:
1587:
1584:
1581:
1578:
1575:
1572:
1569:
1557:
1554:
1510:
1498:
1497:
1485:
1482:
1479:
1476:
1473:
1470:
1467:
1447:
1444:
1441:
1438:
1435:
1432:
1429:
1426:
1423:
1403:
1383:
1380:
1377:
1374:
1371:
1351:
1331:
1328:
1325:
1301:
1281:
1261:
1241:
1221:
1201:
1181:
1161:
1141:
1138:
1135:
1121:
1120:
1108:
1105:
1102:
1099:
1096:
1093:
1090:
1070:
1050:
1047:
1044:
1041:
1038:
1035:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1011:
1008:
1005:
1002:
999:
996:
993:
973:
970:
967:
947:
944:
941:
920:
919:
907:
904:
901:
881:
878:
875:
855:
852:
849:
829:
809:
806:
803:
771:
751:
731:
711:
691:
671:
660:
659:
647:
644:
641:
621:
618:
615:
595:
575:
543:
540:
535:Main article:
532:
529:
528:
527:
519:
513:
507:
441:
438:
424:In the 1950s,
421:
418:
417:
416:
405:
402:
399:
396:
393:
390:
387:
384:
381:
378:
375:
372:
369:
366:
363:
360:
357:
354:
351:
348:
345:
342:
339:
336:
288:
285:
261:expected value
251:described the
245:
242:
240:
237:
187:
183:
162:
140:
136:
113:
109:
105:
100:
96:
92:
89:
86:
83:
80:
77:
74:
71:
56:microeconomics
26:
9:
6:
4:
3:
2:
6050:
6039:
6036:
6034:
6031:
6029:
6026:
6024:
6021:
6019:
6016:
6015:
6013:
5998:
5995:
5993:
5990:
5988:
5985:
5983:
5980:
5978:
5975:
5973:
5972:Risk aversion
5970:
5968:
5965:
5963:
5960:
5958:
5955:
5953:
5950:
5948:
5945:
5943:
5940:
5938:
5935:
5933:
5930:
5928:
5925:
5923:
5920:
5918:
5915:
5913:
5910:
5908:
5905:
5903:
5900:
5899:
5897:
5893:
5887:
5884:
5882:
5879:
5878:
5876:
5872:
5868:
5861:
5856:
5854:
5849:
5847:
5842:
5841:
5838:
5826:
5818:
5816:
5811:
5806:
5805:
5802:
5796:
5793:
5791:
5788:
5784:
5781:
5780:
5779:
5776:
5775:
5773:
5769:
5763:
5760:
5758:
5755:
5753:
5750:
5748:
5745:
5743:
5740:
5738:
5735:
5733:
5730:
5728:
5725:
5723:
5722:Institutional
5720:
5718:
5715:
5713:
5710:
5708:
5705:
5703:
5700:
5698:
5695:
5693:
5690:
5688:
5685:
5683:
5680:
5678:
5675:
5673:
5670:
5668:
5667:Computational
5665:
5663:
5660:
5658:
5655:
5654:
5652:
5648:
5642:
5639:
5635:
5632:
5630:
5627:
5626:
5625:
5622:
5620:
5617:
5613:
5612:Law of supply
5609:
5606:
5604:
5603:Law of demand
5600:
5597:
5596:
5595:
5592:
5590:
5589:Social choice
5587:
5585:
5582:
5580:
5577:
5575:
5574:Excess supply
5571:
5568:
5566:
5563:
5561:
5560:Risk aversion
5558:
5556:
5553:
5551:
5548:
5546:
5543:
5541:
5538:
5536:
5533:
5531:
5528:
5524:
5521:
5519:
5515:
5512:
5510:
5507:
5505:
5502:
5500:
5497:
5495:
5494:Price ceiling
5492:
5490:
5487:
5486:
5485:
5482:
5480:
5477:
5475:
5472:
5468:
5465:
5463:
5460:
5458:
5455:
5451:
5450:Complementary
5448:
5446:
5443:
5442:
5441:
5438:
5436:
5433:
5429:
5426:
5424:
5421:
5420:
5419:
5416:
5415:
5414:
5411:
5409:
5406:
5404:
5401:
5399:
5396:
5394:
5391:
5389:
5386:
5384:
5381:
5379:
5376:
5372:
5369:
5367:
5364:
5363:
5362:
5359:
5357:
5354:
5352:
5349:
5347:
5344:
5340:
5337:
5336:
5335:
5332:
5328:
5325:
5323:
5320:
5318:
5315:
5313:
5310:
5309:
5308:
5305:
5303:
5300:
5298:
5295:
5293:
5290:
5288:
5285:
5283:
5280:
5276:
5273:
5271:
5268:
5266:
5263:
5259:
5256:
5255:
5254:
5251:
5249:
5246:
5244:
5241:
5240:
5239:
5236:
5234:
5233:non-convexity
5230:
5227:
5225:
5222:
5220:
5217:
5215:
5212:
5211:
5209:
5205:
5201:
5194:
5189:
5187:
5182:
5180:
5175:
5174:
5171:
5162:
5157:
5153:
5149:
5144:
5139:
5135:
5131:
5127:
5123:
5118:
5113:
5109:
5105:
5101:
5096:
5092:
5088:
5084:
5080:
5076:
5072:
5067:
5063:
5058:
5054:
5050:
5046:
5042:
5038:
5034:
5029:
5025:
5021:
5017:
5013:
5009:
5005:
5001:
4997:
4992:
4985:
4981:
4974:
4970:
4966:
4962:
4958:
4954:
4950:
4945:
4941:
4936:
4935:
4929:
4928:Martin Shubik
4925:
4922:
4918:
4913:
4909:
4905:
4901:
4897:
4893:
4889:
4885:
4879:
4875:
4871:
4867:
4866:Morgenstern O
4863:
4859:
4855:
4851:
4847:
4846:
4841:
4840:
4835:
4831:
4830:
4825:
4821:
4817:
4813:
4809:
4805:
4801:
4797:
4793:
4788:
4784:
4778:
4773:
4772:
4765:
4764:
4751:
4745:
4741:
4737:
4733:
4726:
4718:
4714:
4710:
4706:
4705:
4697:
4689:
4685:
4681:
4677:
4676:
4668:
4659:
4654:
4650:
4646:
4642:
4638:
4631:
4623:
4619:
4614:
4609:
4604:
4599:
4595:
4591:
4587:
4580:
4572:
4568:
4564:
4560:
4556:
4552:
4545:
4543:
4532:
4526:
4522:
4518:
4513:
4509:
4505:
4501:
4497:
4492:
4488:
4483:
4482:
4477:
4463:
4459:
4453:
4445:
4441:
4437:
4433:
4429:
4425:
4418:
4411:
4403:
4399:
4395:
4391:
4384:
4376:
4372:
4365:
4357:
4353:
4349:
4345:
4341:
4337:
4333:
4329:
4322:
4313:
4305:
4301:
4297:
4293:
4289:
4285:
4278:
4270:
4264:
4256:
4249:
4241:
4237:
4233:
4229:
4222:
4214:
4210:
4206:
4202:
4198:
4194:
4187:
4179:
4175:
4171:
4167:
4160:
4152:
4148:
4144:
4140:
4136:
4132:
4125:
4116:
4115:
4106:
4098:
4094:
4089:
4084:
4080:
4076:
4072:
4065:
4063:
4061:
4053:
4047:
4043:
4039:
4035:
4028:
4020:
4016:
4012:
4008:
4004:
4000:
3996:
3992:
3985:
3977:
3973:
3969:
3965:
3961:
3957:
3950:
3948:
3939:
3926:
3918:
3911:
3903:
3896:
3889:
3881:
3877:
3873:
3869:
3862:
3855:
3847:
3841:
3837:
3833:
3829:
3822:
3820:
3818:
3809:
3805:
3801:
3797:
3793:
3789:
3785:
3781:
3774:
3767:
3753:
3749:
3743:
3739:
3729:
3726:
3724:
3721:
3719:
3716:
3714:
3713:Risk aversion
3711:
3709:
3706:
3704:
3701:
3699:
3696:
3694:
3691:
3689:
3686:
3684:
3683:Loss function
3681:
3679:
3676:
3674:
3671:
3669:
3666:
3664:
3661:
3659:
3656:
3654:
3651:
3649:
3646:
3645:
3635:
3632:
3629:
3625:
3624:
3623:
3615:
3613:
3602:
3600:
3596:
3591:
3587:
3585:
3581:
3577:
3573:
3569:
3565:
3561:
3557:
3553:
3548:
3545:
3541:
3537:
3533:
3529:
3525:
3516:
3512:
3510:
3506:
3505:rule of Bayes
3503:, namely the
3502:
3497:
3487:
3483:
3481:
3477:
3472:
3470:
3466:
3462:
3458:
3453:
3451:
3447:
3443:
3432:
3430:
3426:
3423:presented by
3422:
3412:
3408:
3406:
3402:
3377:
3370:
3367:
3358:
3351:
3348:
3344:
3338:
3335:
3329:
3306:
3305:
3304:
3301:
3287:
3264:
3255:
3248:
3245:
3236:
3229:
3226:
3219:
3216:
3210:
3187:
3186:
3185:
3183:
3179:
3175:
3170:
3167:
3166:risk attitude
3163:
3159:
3153:
3152:Risk aversion
3146:Risk aversion
3143:
3139:
3137:
3133:
3129:
3113:
3110:
3082:
3079:
3073:
3070:
3064:
3061:
3057:
3050:
3020:
3012:
3002:
2999:
2996:
2992:
2988:
2985:
2982:
2974:
2972:
2953:
2947:
2941:
2938:
2932:
2929:
2925:
2918:
2907:
2901:
2895:
2892:
2888:
2884:
2881:
2875:
2869:
2863:
2861:
2842:
2836:
2830:
2827:
2821:
2818:
2812:
2806:
2800:
2797:
2793:
2786:
2780:
2777:
2771:
2765:
2759:
2757:
2744:
2741:
2738:
2734:
2727:
2721:
2718:
2712:
2706:
2700:
2698:
2687:
2681:
2675:
2661:
2660:
2659:
2657:
2653:
2632:
2629:
2626:
2622:
2618:
2615:
2612:
2609:
2603:
2597:
2590:
2589:
2588:
2586:
2583:or otherwise
2582:
2578:
2574:
2564:
2551:
2548:
2540:
2521:
2515:
2492:
2489:
2486:
2479:
2473:
2467:
2461:
2448:
2444:
2440:
2431:
2425:
2419:
2409:
2408:
2407:
2393:
2384:
2370:
2365:
2361:
2338:
2334:
2308:
2304:
2297:
2289:
2271:
2267:
2243:
2240:
2232:
2228:
2221:
2218:
2213:
2209:
2205:
2197:
2193:
2186:
2183:
2178:
2174:
2170:
2161:
2155:
2149:
2139:
2138:
2137:
2135:
2117:
2113:
2092:
2078:
2076:
2071:
2058:
2055:
2052:
2049:
2046:
2026:
2023:
2020:
1995:
1991:
1987:
1984:
1978:
1972:
1965:
1964:
1963:
1946:
1943:
1940:
1934:
1931:
1928:
1925:
1902:
1899:
1896:
1890:
1887:
1862:
1858:
1854:
1848:
1842:
1835:
1834:
1833:
1813:
1807:
1804:
1801:
1795:
1789:
1782:
1781:
1780:
1777:
1761:
1758:
1755:
1751:
1747:
1725:
1722:
1719:
1715:
1711:
1689:
1686:
1683:
1679:
1675:
1672:
1646:
1643:
1640:
1636:
1632:
1629:
1623:
1617:
1610:
1609:
1608:
1591:
1585:
1582:
1579:
1573:
1567:
1553:
1551:
1547:
1543:
1539:
1535:
1530:
1526:
1524:
1508:
1480:
1477:
1474:
1468:
1465:
1445:
1439:
1436:
1433:
1427:
1424:
1421:
1401:
1381:
1378:
1375:
1372:
1369:
1349:
1329:
1326:
1323:
1315:
1314:
1313:
1299:
1279:
1259:
1239:
1219:
1199:
1179:
1159:
1139:
1136:
1133:
1125:
1103:
1100:
1097:
1091:
1088:
1068:
1048:
1045:
1039:
1036:
1033:
1027:
1024:
1021:
1018:
1015:
1009:
1006:
1003:
997:
994:
991:
971:
968:
965:
945:
942:
939:
931:
930:
929:
926:
925:
905:
902:
899:
892:we must have
879:
876:
873:
853:
850:
847:
827:
807:
804:
801:
793:
792:
791:
789:
788:
783:
769:
749:
729:
709:
689:
669:
645:
642:
639:
619:
616:
613:
593:
573:
565:
564:
563:
561:
560:
555:
553:
549:
538:
525:
524:
520:
517:
516:Consequences:
514:
511:
508:
505:
502:
501:
500:
497:
495:
491:
487:
483:
479:
475:
471:
467:
463:
459:
455:
451:
447:
437:
433:
429:
427:
397:
391:
388:
382:
376:
364:
358:
355:
352:
346:
340:
334:
327:
326:
325:
307:
303:
298:
294:
284:
282:
278:
273:
270:
266:
265:risk aversion
262:
258:
254:
250:
239:Justification
236:
234:
230:
226:
222:
216:
214:
210:
205:
203:
185:
181:
160:
138:
134:
111:
107:
98:
94:
87:
84:
81:
75:
69:
59:
57:
53:
49:
45:
41:
37:
33:
19:
5880:
5757:Optimization
5742:Mathematical
5702:Experimental
5697:Evolutionary
5682:Econometrics
5628:
5540:Public goods
5514:Price system
5509:Price signal
5423:Monopolistic
5292:Distribution
5207:Major topics
5160:
5107:
5103:
5074:
5070:
5061:
5039:(1): 69â78.
5036:
5032:
5019:
4999:
4995:
4984:the original
4979:
4960:
4948:
4933:
4907:
4903:
4873:
4853:
4850:de Finetti B
4838:
4834:de Finetti B
4823:
4820:de Finetti B
4811:
4807:
4804:de Finetti B
4795:
4791:
4770:
4731:
4725:
4708:
4702:
4696:
4679:
4673:
4667:
4643:(1): 46â55.
4640:
4636:
4630:
4593:
4589:
4579:
4554:
4550:
4520:
4516:
4507:
4504:Amos Tversky
4486:
4476:
4465:. Retrieved
4461:
4452:
4427:
4424:Econometrica
4423:
4410:
4393:
4389:
4383:
4374:
4364:
4334:(1): 69â78.
4331:
4327:
4321:
4312:
4287:
4284:Econometrica
4283:
4277:
4254:
4248:
4231:
4227:
4221:
4196:
4192:
4186:
4169:
4165:
4159:
4134:
4130:
4124:
4113:
4105:
4078:
4074:
4033:
4027:
3994:
3990:
3984:
3959:
3955:
3925:cite journal
3910:
3901:
3888:
3871:
3867:
3854:
3827:
3786:(1): 79â88.
3783:
3779:
3766:
3755:. Retrieved
3751:
3742:
3621:
3608:
3588:
3549:
3522:
3513:
3493:
3484:
3473:
3461:Amos Tversky
3454:
3438:
3418:
3409:
3398:
3302:
3279:
3181:
3177:
3171:
3155:
3140:
3131:
3127:
3039:
2655:
2651:
2649:
2570:
2507:
2385:
2287:
2258:
2105:whose value
2084:
2072:
2012:
1879:
1831:
1778:
1663:
1559:
1549:
1545:
1531:
1527:
1499:
1123:
1122:
922:
921:
787:Transitivity
786:
784:
661:
559:Completeness
558:
556:
551:
545:
522:
521:
515:
509:
503:
498:
493:
489:
485:
481:
477:
473:
469:
465:
461:
457:
453:
449:
443:
434:
430:
423:
293:Frank Ramsey
290:
274:
269:risk premium
267:, where the
247:
217:
206:
201:
173:with payoff
60:
31:
29:
6023:Game theory
5977:Game theory
5707:Game theory
5672:Development
5619:Uncertainty
5499:Price floor
5479:Preferences
5418:Competition
5388:Information
5351:Externality
5334:Equilibrium
5275:Transaction
5253:Opportunity
5214:Aggregation
4921:von Neumann
4917:Morgenstern
4500:Paul Slovic
3893:Elliott E.
3599:hyperpriors
3552:uncertainty
3300:is wealth.
3158:risk-averse
3134:. See also
548:four axioms
297:preferences
44:uncertainty
38:concerning
6012:Categories
5737:Managerial
5657:Behavioral
5530:Production
5467:Oligopsony
5307:Elasticity
5219:Budget set
5008:Davidson D
5002:: 529â563.
4808:Erkenntnis
4658:1794/22312
4467:2021-04-28
4137:(1): 1â4.
3868:Dialectica
3757:2021-04-28
3735:References
3626:Theory of
3532:irrational
1534:set theory
1124:Continuity
958:such that
546:There are
5874:Decisions
5778:Economics
5650:Subfields
5545:Rationing
5462:Oligopoly
5457:Monopsony
5445:Bilateral
5378:Household
5229:Convexity
5117:1011.4404
5091:224830682
4969:Ramsey RP
4896:Jastrow J
4892:Peirce CS
4798:: 941â73.
4571:0304-4068
4348:0346-1238
4263:cite book
4097:0013-0133
4019:164842618
4011:0025-5572
3976:0162-1459
3800:0304-4076
3564:sensitive
3560:ambiguity
3474:Like any
3435:Criticism
3339:−
3220:−
3080:
3074:−
3062:−
3051:
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