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Behavioral strategies, which include cooperation, defection, and cooperation coupled with punishment, are chosen in alignment with the agent's prevailing learning rule. Simulations of the model under conditions approximating those experienced by early hominids reveal that conformism can evolve even when individuals are solely faced with a cooperative dilemma, contrary to previous assertions. Moreover, the incorporation of conformists significantly amplifies the group size within which cooperation can be sustained. These model results demonstrate robustness, maintaining validity even under conditions of high migration rates and infrequent intergroup conflicts.
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each round was determined by that strategy's success in the previous round. The competition in each round becomes stronger as weaker performers are reduced and eliminated. The results were amazing: a handful of strategies – all "nice" – came to dominate the field. In a sea of non-nice strategies the "nice" strategies – provided they were also provocable – did well enough with each other to offset the occasional exploitation. As cooperation became general the non-provocable strategies were exploited and eventually eliminated, whereupon the exploitive (non-cooperating) strategies were out-performed by the cooperative strategies.
108:
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that is, the players have a negligible chance of meeting again – each interaction is effectively a single-shot
Prisoner's Dilemma game, and one might as well defect in all cases (a strategy called "ALL D"), because even if one cooperates there is no way to keep the other player from exploiting that. But in the iterated PD the value of repeated cooperative interactions can become greater than the benefit/risk of single exploitation (which is all that a strategy like TFT will tolerate).
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466:" (TFT) that cooperates on the first move, and subsequently echoes (reciprocates) what the other player did on the previous move. The results of the first tournament were analyzed and published, and a second tournament was held to see if anyone could find a better strategy. TFT won again. Axelrod analyzed the results and made some interesting discoveries about the nature of cooperation, which he describes in his book.
33:
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because altruistic or parochial behavior reduces one's payoffs by comparison to what one would gain from eschewing these behaviors. But parochial altruism could have evolved if parochialism promoted intergroup hostilities and the combination of altruism and parochialism contributed to success in these conflicts.... would have been viable singly, but by promoting group conflict they could have evolved jointly.
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540:. (The "futility of isolated revolt".) But another finding of great significance is that clusters of nice strategies can get established. Even a small group of individuals with nice strategies with infrequent interactions can yet do so well on those interactions to make up for the low level of exploitation from non-nice strategies.
262:
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and Karl
Sigmund demonstrated a strategy called Pavlov (or "win–stay, lose–shift") that does better in these circumstances. Pavlov looks at its own prior move as well as the other player's move. If the payoff was R or P (see "Prisoner's Dilemma", above) it cooperates; if S or T it defects.
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generally, they do poorly. "A common problem with these rules is that they used complex methods of making inferences about the other player – and these inferences were wrong." Against TFT one can do no better than to simply cooperating. Axelrod calls this "clarity". Or: "don't be too clever".
608:
When an IPD tournament introduces noise (errors or misunderstandings), TFT strategies can get trapped into a long string of retaliatory defections, thereby depressing their score. TFT also tolerates "ALL C" (always cooperate) strategies, which then give an opening to exploiters. In 1992 Martin Nowak
653:
Neither Choi & Bowles nor Guzmán, Rodriguez-Sicket and
Rowthorn claim that humans have actually evolved in this way, but that computer simulations show how war could be promoted by the interaction of these behaviors. A crucial open research question, thus, is how realistic the assumptions are on
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The success of any strategy depends on the nature of the particular strategies it encounters, which depends on the composition of the overall population. To better model the effects of reproductive success
Axelrod also did an "ecological" tournament, where the prevalence of each type of strategy in
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Being "nice" can be beneficial, but it can also lead to being suckered. To obtain the benefit – or avoid exploitation – it is necessary to be provocable and forgiving. When the other player defects, a nice strategy must immediately be provoked into retaliatory defection. The same goes
527:
Curiously, rationality and deliberate choice are not necessary, nor trust nor even consciousness, as long as there is a pattern that benefits both players (e.g., increases fitness), and some probability of future interaction. Often the initial mutual cooperation is not even intentional, but having
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The lessons described above apply in environments that support cooperation, but whether cooperation is supported at all, depends crucially on the probability (called ω ) that the players will meet again, also called the discount parameter or, figuratively, the shadow of the future. When ω is low –
469:
In both actual tournaments and various replays, the best-performing strategies were nice: that is, they were never the first to defect. Many of the competitors went to great lengths to gain an advantage over the "nice" (and usually simpler) strategies, but to no avail: tricky strategies fighting
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Consideration of the mechanisms through which learning from the social environment occurs is pivotal in studies of evolution. In the context of this discussion, learning rules, specifically conformism and payoff-dependent imitation, are not arbitrarily predetermined but are biologically selected.
493:
In any IPD game, there is a certain maximum score each player can get by always cooperating. But some strategies try to find ways of getting a little more with an occasional defection (exploitation). This can work against some strategies that are less provocable or more forgiving than TFT, but
636:
which exhibit some of the properties observed in empirical networks If network structure and choices in the
Prisoner's dilemma co-evolve, then cooperation can survive. In the resulting networks cooperators will be more centrally located than defectors who will tend to be in the periphery of the
627:
The payoffs in the
Prisoner's Dilemma game are fixed, but in real life defectors are often punished by cooperators. Where punishment is costly there is a second-order dilemma amongst cooperators between those who pay the cost of enforcement and those who do not. Other work has shown that while
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Even when the discount parameter ω is high enough to permit reciprocal cooperation there is still a question of whether and how cooperation might start. One of
Axelrod's findings is that when the existing population never offers cooperation nor reciprocates it – the case of ALL D – then no nice
644:
Altruism—benefiting fellow group members at a cost to oneself —and parochialism—hostility towards individuals not of one's own ethnic, racial, or other group—are common human behaviors. The intersection of the two—which we term "parochial altruism"—is puzzling from an evolutionary perspective
531:
This implies two requirements for the players, aside from whatever strategy they may adopt. First, they must be able to recognize other players, to avoid exploitation by cheaters. Second, they must be able to track their previous history with any given player, in order to be responsive to that
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for a few points generally could not do as well as nice strategies working together. TFT (and other "nice" strategies generally) "won, not by doing better than the other player, but by eliciting cooperation by promoting the mutual interest rather than by exploiting the other's weakness."
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In small populations or groups there is the possibility that indirect reciprocity (reputation) can interact with direct reciprocity (e.g. tit for tat) with neither strategy dominating the other. The interactions between these strategies can give rise to dynamic
485:
score higher than its partner; at best it can only do "as good as". Yet it won the tournaments by consistently scoring a strong second-place with a variety of partners. Axelrod summarizes this as "don't be envious"; in other words, don't strive for a payoff
1601:
Phelps, S., Nevarez, G. & Howes, A., 2009. The effect of group size and frequency of encounter on the evolution of cooperation. In LNCS, Volume 5778, ECAL 2009, Advances in
Artificial Life: Darwin meets Von Neumann. Budapest: Springer, pp. 37–44.
577:. Other work on the evolution of cooperation has expanded to cover prosocial behavior generally, and in religion, other mechanisms for generating cooperation, the IPD under different conditions and assumptions, and the use of other games such as the
628:
individuals given a choice between joining a group that punishes free-riders and one that does not initially prefer the sanction-free group, yet after several rounds they will join the sanctioning group, seeing that sanctions secure a better payoff.
442:. The book provides a detailed explanation of the evolution of cooperation, beyond traditional game theory. Academic literature regarding forms of cooperation that are not easily explained in traditional game theory, especially when considering
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Cooperation becomes more complicated, however, as soon as more realistic models are assumed that for instance offer more than two choices of action, provide the possibility of gradual cooperation, make actions constrain future actions
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for forgiveness: return to cooperation as soon as the other player does. Overdoing the punishment risks escalation, and can lead to an "unending echo of alternating defections" that depresses the scores of both players.
481:" – that is, the total rewards are fixed, and a player does well only at the expense of other players. But real life is not zero-sum. Our best prospects are usually in cooperative efforts. In fact, TFT
616:
Indirect reciprocity is based on knowing the other player's reputation, which is the player's history with other players. Cooperation depends on a reliable history being projected from past partners to future
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Most of these references are to the scientific literature, to establish the authority of various points in the article. A few references of lesser authority, but greater accessibility are also included.
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and
Michael Cohen use computer simulations to show cooperation rising among agents who have negligible chance of future encounters but can recognize similarity of an arbitrary characteristic (such as a
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de
Quervain, D. J.-F.; Fischbacker, Urs; Treyer, Valerie; Schellhammer, Melanie; Schnyder, Ulrich; Buck, Alfred; Fehr, Ernst (24 August 2004), "The Neural Basis of Altruistic Punishment",
596:
Nice strategies are better able to invade if they have social structures or other means of increasing their interactions. Axelrod discusses this in chapter 8; in a later paper he and
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Axelrod initially solicited strategies from other game theorists to compete in the first tournament. Each strategy was paired with each other strategy for 200 iterations of a
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605:); whereas other studies have shown that the only Iterated Prisoner's Dilemma strategies that resist invasion in a well-mixed evolving population are generous strategies.
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Rusch, Hannes (2014), "The Evolutionary Interplay of Intergroup Conflict and Altruism in Humans: A Review of Parochial Altruism Theory and Prospects for its Extension",
2147:
612:
In a 2006 paper Nowak listed five mechanisms by which natural selection can lead to cooperation. In addition to kin selection and direct reciprocity, he shows that:
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alone were "growing at the rate of over 300 per year". To fully review this literature is infeasible. What follows are therefore only a few selected highlights.
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1522:, pp. 136–138) has some interesting comments on the need to suppress universal cooperators. See also a similar theme in Piers Anthony's novel
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Group selection assumes that groups with cooperators (even altruists) will be more successful as a whole, and this will tend to benefit all members.
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Network reciprocity relies on geographical or social factors to increase the interactions with nearer neighbors; it is essentially a virtual group.
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Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.
46:
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17:
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Stewart, Alexander; Plotkin, Joshua B. (17 September 2013), "From extortion to generosity, evolution in the Iterated Prisoner's Dilemma",
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Hofstadter, Douglas R. (May 1983), "Metamagical Themas: Computer Tournaments of the Prisoner's Dilemma Suggest How Cooperation Evolves",
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games to explore deep-seated notions of fairness and fair play. It has also been used to challenge the rational and self-regarding "
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game and scored on the total points accumulated through the tournament. The winner was a very simple strategy submitted by
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Don't be envious: focus on maximizing your own 'score', as opposed to ensuring your score is higher than your 'partner's'.
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548:), or in which interpret the associate's actions are is non-trivial (e.g. recognizing the degree of cooperation shown)
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446:, largely took its modern form as a result of Axelrod's and Hamilton's influential 1981 paper and the subsequent book.
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1679:"When in Rome, do as the Romans do: the coevolution of altruistic punishment, conformist learning, and cooperation"
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Axelrod's book was summarized in Douglas Hofstadter's May 1983 "Metamagical Themas" column in Scientific American (
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412:. The article's summary addresses the issue in terms of "cooperation in organisms, whether bacteria or primates".
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Hofstadter, Douglas R. (1985), "The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation",
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Axelrod, Robert (1997), "The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration",
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Axelrod, Robert (1997), "The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration",
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The source code for the second tournament run by Robert Axelrod (written by Axelrod and many contributors in
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Poundstone, William (1992), "Prisoner's Dilemma: John von Neumann, Game Theory and the Puzzle of the Bomb",
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In "The Coevolution of Parochial Altruism and War" by Jung-Kyoo Choi and Samuel Bowles. From their summary:
528:"discovered" a beneficial pattern both parties respond to it by continuing the conditions that maintain it.
375:
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Sanfey, Alan G. (26 October 2007), "Social Decision-Making: Insights from Game Theory and Neuroscience",
680:
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Don't be too clever: or, don't try to be tricky. Clarity is essential for others to cooperate with you.
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Hauert, Christoph; Traulsen, Arne; Brandt, Hannelore; Nowak, Martin A.; Sigmund, Karl (29 June 2007),
88:
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Morse, Phillip M.; Kimball, George E. (1956), "How to Hunt a Submarine", in Newman, James R. (ed.),
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Choi, Jung-Kyoo; Bowles, Samuel (26 October 2007), "The Coevolution of Parochial Altruism and War",
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In 1984 Axelrod estimated that there were "hundreds of articles on the Prisoner's Dilemma cited in
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In summary, success in an evolutionary "game" correlated with the following characteristics:
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that expands upon a paper of the same name written by Axelrod and evolutionary biologist
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Von Neumann, John; Morgenstern, Oskar (1944), "Theory of Games and Economic Behavior",
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3177:"A strategy of win-stay, lose-shift that outperforms tit for tat in Prisoner's Dilemma"
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Vogel, Gretchen (20 February 2004), "News Focus: The Evolution of the Golden Rule",
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Vogel, Gretchen (20 February 2004), "News Focus: The Evolution of the Golden Rule",
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strategy can get established by isolated individuals; cooperation is strictly a
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Milinski, Manfred (1 July 1993), "News and Views: Cooperation Wins and Stays",
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2030:"Group Competition, Reproductive Leveling, and the Evolution of Human Altruism"
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3401:"Reproductive Social Behavior: Cooperative Games to Replace Sexual Selection"
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1995:
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Here group selection is not a form of evolution, which is problematical (see
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Be provocable: return defection for defection, cooperation for cooperation.
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The Compleat Strategyst: being a primer on the theory of games of strategy
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2533:
1940:
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10.1002/(SICI)1099-0526(199801/02)3:3<46::AID-CPLX6>3.0.CO;2-K
1330:"INCA: A multi-choice model of cooperation under restricted communication"
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10.1002/(SICI)1099-0526(199801/02)3:3<46::AID-CPLX6>3.0.CO;2-K
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Riolo, Rick L.; Cohen, Michael D.; Axelrod, Robert (23 November 2001),
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Gürerk, Özgür; Irlenbusch, Bernd; Rockenbach, Bettina (7 April 2006),
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Most of the games that game theory had heretofore investigated are "
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Nowak, Martin A; Page, Karen M.; Sigmund, Karl (8 September 2000),
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Maynard Smith, John (September 1978), "The Evolution of Behavior",
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972:
478:
3745:"Scientist Finds the Beginnings of Morality in Primitive Behavior"
2647:"Cooperation, Punishment, and the Evolution of Human Institutions"
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Hardin, Garrett (13 December 1968), "The Tragedy of the Commons",
2090:"The co-evolution of individual behaviors and social institutions"
1617:"Emergence of social networks via direct and indirect reciprocity"
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Maynard Smith, John (1976), "Evolution and the Theory of Games",
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3800:
The Iterated Prisoner's Dilemma and The Evolution of Cooperation
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Metamagical Themas: Questing for the Essence of Mind and Pattern
1676:
427:. Since 2006, reprints of the book have included a foreword by
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Sigmund, Karl; Fehr, Ernest; Nowak, Martin A. (January 2002),
1087:); see also Richard Dawkin's summary in the second edition of
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Sigmund, Karl; Fehr, Ernest; Nowak, Martin A. (January 2002),
2586:"Via Freedom to Coercion: The Emergence of Costly Punishment"
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1103:
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589:" model of economics, and as a basis for replacing Darwinian
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Bowles, Samuel; Choi, Jung-Koo; Hopfensitz, Astrid (2003),
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Guzmán, R. A.; Rodríguez-Sickert, C.; Rowthorn, R. (2007).
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can emerge and persist as explained by the application of
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2758:"Twenty Years on: The Evolution of Cooperation Revisited"
2342:"Cooperation through Imitation and Exclusion in Networks"
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Game Theory and the Social Contract: Vol. 2, Just Playing
1949:
Game Theory and the Social Contract: Vol. 1, Playing Fair
2311:(A Facsimile of the First ed.), Harvard Univ. Press
1569:, ch. 7), but a mechanism for evolving cooperation.
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Proceedings of the Royal Society B: Biological Sciences
2405:"The Competitive Advantage of Sanctioning Institutions"
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Axelrod, Robert; Hamilton, William D. (27 March 1981),
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Axelrod, Robert; Hamilton, William D. (27 March 1981),
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1843:
Annotated Bibliography on the Evolution of Cooperation
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Journal of Artificial Societies and Social Simulation
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1486:
2955:"The Origin and Evolution of Religious Prosociality"
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Norenzayan, Ara; Shariff, Azim F. (3 October 2008),
2206:"When Does 'Economic Man' Dominate Social Behavior?"
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1029:
449:
3116:Nowak, Martin A.; Sigmund, Karl (16 January 1992),
2948:, vol. 4, Simon and Schuster, pp. 2160–79
3778:(25th Anniversary ed.), Harvard Univ. Press,
3318:The Virtue of Selfishness: A New Concept of Egoism
1853:Axelrod, Robert; Dion, Douglas (9 December 1988),
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2952:
2204:Camerer, Colin F.; Fehr, Ernst (6 January 2006),
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505:Be nice: cooperate, never be the first to defect.
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3590:Proceedings of the National Academy of Sciences
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3175:Nowak, Martin A.; Sigmund, Karl (1 July 1993),
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1111:
3587:
3336:"Evolution of cooperation without reciprocity"
3271:
3067:"Fairness Versus Reason in the Ultimatum Game"
2926:Morse, Phillip M.; Kimball, George E. (1951),
2842:, vol. 239, no. 3, pp. 176–92,
431:and have been marketed as a revised edition.
415:The book details a theory on the emergence of
404:is a 1984 book written by political scientist
3552:, vol. 286, no. 1, pp. 82–87,
3325:Rapoport, Anatol; Chammah, Albert M. (1965),
3006:"Five Rules for the Evolution of Cooperation"
2869:
2837:
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2696:Henrich, Joseph; et al. (23 June 2007),
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2257:The Gospel of Wealth, and Other Timely Essays
914:, vol. 286, no. 1, pp. 82–87,
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2826:, vol. 61, no. 1, pp. 41–45,
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2499:"The Genetical Evolution of Social Behavior"
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434:The book provides an investigation into how
199:. There might be a discussion about this on
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61:Learn how and when to remove these messages
3462:, E. P. Dutton & Co. (published 1950)
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2775:
2698:"Costly Punishment Across Human Societies"
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1840:Axelrod, Robert; D'Ambrosio, Lisa (1996),
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1449:categorizes and summarizes over 50 studies
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593:theory with a theory of social selection.
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3118:"Tit For Tat in Heterogenous Populations"
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1968:Review of 'The Complexity of Cooperation'
1826:(Revised ed.), Perseus Books Group,
1624:Autonomous Agents and Multi-Agent Systems
772:(Revised ed.), Perseus Books Group,
654:which these simulation models are based.
237:Learn how and when to remove this message
219:Learn how and when to remove this message
160:Learn how and when to remove this message
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2349:Journal of Economic Dynamics and Control
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1964:
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1767:(3), Princeton University Press: 46–48,
1591:Gürerk, Irlenbusch & Rockenbach 2006
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796:(3), Princeton University Press: 46–48,
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1789:"On Six Advances in Cooperation Theory"
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3812:
3773:
3638:"The Evolution of Reciprocal Altruism"
3504:
2746:
2547:
2464:"The Evolution of Altruistic Behavior"
2306:
2027:
2009:
1855:"The Further Evolution of Cooperation"
1614:
1406:
954:"The Evolution of Reciprocal Altruism"
696:
3670:
3466:
3003:
2802:
2385:
1977:"Reciprocity and the social contract"
1718:
1553:
1430:
3769:(2nd ed.), McGraw-Hill Book Co.
3742:
3715:(3981), Princeton Univ. Press: 172,
3315:
2805:Hobbesian moral and political theory
2322:(2nd ed.), Oxford Univ. Press,
2145:
1984:Politics, Philosophy & Economics
1402:
834:(2nd ed.), Oxford Univ. Press,
519:Foundation of reciprocal cooperation
171:
116:
67:
26:
3825:Books about evolutionary psychology
3004:Nowak, Martin A (8 December 2006),
2379:Morality and Rational Self-Interest
1487:Roughgarden, Oishi & Akcay 2006
560:", and estimated that citations to
24:
3399:; Akcay, Erol (17 February 2006),
2856:10.1038/scientificamerican0978-176
2028:Bowles, Samuel (8 December 2006),
1706:10.1016/j.evolhumbehav.2006.08.002
551:
419:between individuals, drawing from
132:tone or style may not reflect the
25:
3851:
3793:
3636:Trivers, Robert L. (March 1971),
3566:10.1038/scientificamerican0102-82
2883:, Bobbs-Merrill (published 1977)
2872:Evolution and the Theory of Games
2815:Mutual Aid: A Factor in Evolution
2789:, Basic Books, pp. 715–730,
2751:, Bobbs-Merrill (published 1958)
2012:Evolution: The History of an Idea
952:Trivers, Robert L. (March 1971),
928:10.1038/scientificamerican0102-82
872:Mutual Aid: A Factor of Evolution
450:Background: Axelrod's tournaments
42:This article has multiple issues.
3743:Wade, Nicholas (20 March 2007),
2645:Henrich, Joseph (7 April 2006),
2386:Gould, Stephen Jay (June 1997),
2377:Gauthier, David P., ed. (1970),
2146:Boyd, Robert (8 December 2006),
1046:
1032:
850:Gould, Stephen Jay (June 1997),
176:
142:guide to writing better articles
121:
106:
72:
31:
3776:Sociobiology: The New Synthesis
3458:Rousseau, Jean Jacques (1762),
2780:, vol. 248, pp. 16–26
2148:"The Puzzle of Human Sociality"
1727:
1712:
1670:
1658:
1608:
1595:
1584:
1572:
1559:
1547:
1531:
1513:
1504:
1499:Riolo, Cohen & Axelrod 2001
1492:
1480:
1468:
1452:
1436:
1424:
1412:
1396:
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1372:
1360:
1321:
1309:
1297:
1285:
1273:
1261:
1249:
1237:
1225:
1213:
1201:
50:or discuss these issues on the
2928:Methods of Operations Research
2506:Journal of Theoretical Biology
2097:Journal of Theoretical Biology
1906:"The Evolution of Cooperation"
1463:Sigmund, Fehr & Nowak 2002
1459:Nowak, Page & Sigmund 2000
1189:
1177:
1165:
1153:
1141:
1129:
1117:
1073:
705:"The Evolution of Cooperation"
335:Hardback, paperback, audiobook
13:
1:
3685:10.1126/science.303.5661.1128
3094:10.1126/science.289.5485.1773
2570:10.1126/science.162.3859.1243
2497:Hamilton, William D. (1964),
2462:Hamilton, William D. (1963),
2117:10.1016/S0022-5193(03)00060-2
2014:, Univ. of California Press,
1965:Binmore, Kenneth G. (1998b),
1956:Binmore, Kenneth G. (1998a),
1882:10.1126/science.242.4884.1385
1787:Axelrod, Robert (July 2000),
1419:Norenzayan & Shariff 2008
1067:
1003:10.1126/science.303.5661.1128
570:The Complexity of Cooperation
255:The Evolution of Cooperation
3543:"The Economics of Fair Play"
2870:Maynard Smith, John (1982),
2526:10.1016/0022-5193(64)90038-4
1975:Binmore, Kenneth G. (2004),
1947:Binmore, Kenneth G. (1994),
1824:The Evolution of Cooperation
1743:The Evolution of Cooperation
1686:Evolution and Human Behavior
1354:10.1016/0303-2647(95)01549-3
905:"The Economics of Fair Play"
770:The Evolution of Cooperation
750:The Evolution of Cooperation
575:The Evolution of Cooperation
562:The Evolution of Cooperation
401:The Evolution of Cooperation
85:for non-readers of the book.
18:The evolution of cooperation
7:
3774:Wilson, Edward O. (2000) ,
3645:Quarterly Review of Biology
2388:"Kropotkin was no crackpot"
2368:Gauthier, David P. (1986),
1112:Axelrod & Hamilton 1981
1025:
961:Quarterly Review of Biology
852:"Kropotkin was no crackpot"
657:
251:1984 book by Robert Axelrod
10:
3856:
3765:Williams, John D. (1966),
3756:Williams, John D. (1954),
3320:, The New American Library
3242:(9), Anchor Books: 73–74,
2803:Kavka, Gregory S. (1986),
2361:10.1016/j.jedc.2010.12.002
2316:Dawkins, Richard (1989) ,
1510:Stewart and Plotkin (2013)
1083:) (reprinted in his book (
887:, Viking (Penguin Books),
828:Dawkins, Richard (1989) ,
3329:, Univ. of Michigan Press
2879:Melville, Herman (1851),
2307:Darwin, Charles (1964) ,
2255:Carnegie, Andrew (1900),
2010:Bowler, Peter J. (1984),
1632:10.1007/s10458-012-9207-8
1327:
490:than the other player's.
385:
373:
359:
347:
339:
331:
323:
313:
303:
289:
281:
271:
259:
2946:The World of Mathematics
2812:Kropotkin, Petr (1902),
2756:Hoffman, Robert (2000),
2309:On the Origin of Species
1996:10.1177/1470594X04039981
1822:Axelrod, Robert (2006),
1741:Axelrod, Robert (1984),
1579:Hauert & others 2007
1538:Nowak & Sigmund 1992
1062:Co-operation (evolution)
768:Axelrod, Robert (2006),
748:Axelrod, Robert (1984),
3830:Books about game theory
3758:The Compleat Strategyst
3611:10.1073/pnas.1306246110
3527:10.1126/science.1142996
3428:10.1126/science.1110105
3294:10.1126/science.1100735
3033:10.1126/science.1133755
2982:10.1126/science.1158757
2874:, Cambridge Univ. Press
2807:, Princeton Univ. Press
2747:Hobbes, Thomas (1651),
2725:10.1126/science.1127333
2666:10.1126/science.1126398
2613:10.1126/science.1141588
2432:10.1126/science.1123633
2285:10.1126/science.1144237
2233:10.1126/science.1110600
2167:10.1126/science.1136841
2054:10.1126/science.1134829
1933:10.1126/science.7466396
1653:Fosco & Mengel 2011
1475:Camerer & Fehr 2006
1443:Axelrod & Dion 1988
1328:Prechelt, Lutz (1996).
732:10.1126/science.7466396
679:, a library written in
558:Psychological Abstracts
3820:1984 non-fiction books
3805:The Evolution of Trust
3481:10.1098/rspb.2014.1539
1665:Choi & Bowles 2007
683:, last updated in 1999
647:
1808:10.1515/auk-2000-0107
885:The Origins of Virtue
883:Ridley, Matt (1996),
642:
2372:, Oxford Univ. Press
1796:Analyse & Kritik
1318:, pp. 63–68, 99
573:, to be a sequel to
444:evolutionary biology
425:evolutionary biology
189:confusing or unclear
89:improve this article
3721:1946Natur.157..172R
3602:2013PNAS..11015348S
3596:(38): 15348–15353,
3558:2002SciAm.286a..82S
3550:Scientific American
3519:2007Sci...318..598S
3460:The Social Contract
3420:2006Sci...311..965R
3395:Roughgarden, Joan;
3355:2001Natur.414..441R
3286:2004Sci...305.1254D
3248:1992PhT....45i..73P
3196:1993Natur.364...56N
3137:1985Natur.315..250T
3086:2000Sci...289.1773N
3025:2006Sci...314.1560N
2974:2008Sci...322...58N
2902:1993Natur.364...12M
2848:1978SciAm.239c.176S
2840:Scientific American
2832:1976AmSci..64...41M
2778:Scientific American
2717:2006Sci...312.1767H
2605:2007Sci...316.1905H
2562:1968Sci...162.1243H
2556:(3859): 1243–1248,
2543:on 29 December 2009
2518:1964JThBi...7....1H
2471:American Naturalist
2424:2006Sci...312..108G
2370:Morals by agreement
2277:2007Sci...318..636C
2225:2006Sci...311...47C
2134:on 19 February 2005
2109:2003JThBi.223..135B
2046:2006Sci...314.1569B
1925:1981Sci...211.1390A
1874:1988Sci...242.1385A
1773:1998Cmplx...3c..46C
1698:2007EHumB..28..112A
1346:1996BiSys..37..127P
1282:, pp. 18, 174.
1234:, pp. 47, 118.
1198:, pp. 110–113.
1162:, pp. 62, 211.
920:2002SciAm.286a..82S
912:Scientific American
802:1998Cmplx...3c..46C
724:1981Sci...211.1390A
697:Recommended reading
532:player's strategy.
256:
197:clarify the article
3749:The New York Times
3475:(1794): 20141539,
3327:Prisoner's Dilemma
3316:Rand, Ayn (1961),
2824:American Scientist
2512:(1): 1–16, 17–52,
2338:Mengel, Friederike
2336:Fosco, Constanza;
2192:on 17 October 2018
2076:on 7 February 2009
1615:Phelps, S (2012).
869:Kropotkin, Peter.
456:Prisoner's Dilemma
254:
3840:Basic Books books
3679:(5661): 1128–31,
3513:(5850): 598–602,
3256:10.1063/1.2809809
3131:(6016): 250–253,
3080:(5485): 1773–75,
3019:(5805): 1560–63,
2930:, The MIT Press,
2711:(5781): 1767–70,
2599:(5833): 1905–07,
2161:(5805): 1555–56,
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1919:(4489): 1390–96,
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209:October 2011
206:
195:Please help
186:
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97:October 2011
94:
87:Please help
82:
58:
51:
45:
44:Please help
41:
2138:23 February
2080:23 February
1960:, MIT Press
1951:, MIT Press
1802:: 130–151,
1540:; see also
1407:Bowles 2006
603:green beard
464:tit for tat
440:game theory
436:cooperation
421:game theory
417:cooperation
308:Basic Books
3814:Categories
2271:: 636–40,
1761:Complexity
1719:Rusch 2014
1554:Nowak 2006
1525:Macroscope
1431:Nowak 2006
1334:Biosystems
1095:, ch. 12).
1068:References
790:Complexity
598:Rick Riolo
538:sucker bet
319:April 1984
294:Philosophy
266:Book cover
191:to readers
47:improve it
3701:178426383
3651:: 35–57,
2881:Moby-Dick
2749:Leviathan
2004:144880524
1403:Boyd 2006
1019:178426383
967:: 35–57,
637:network.
617:partners.
583:Ultimatum
304:Publisher
298:sociology
150:July 2019
53:talk page
3737:29754824
3693:14976292
3665:19027999
3630:24003115
3574:11799620
3535:17962552
3499:25253457
3444:32364112
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3381:11719803
3302:15333831
3102:10976075
3051:17158317
2990:18832637
2733:16794075
2682:39232348
2674:16601179
2631:17600218
2491:84216415
2448:40038573
2440:16601192
2340:(2011).
2293:17962562
2241:16400140
2183:86630847
2175:17158313
2125:12814597
2062:17158320
1898:41453503
1890:17802133
1816:17399009
1026:See also
1011:14976292
981:19027999
936:11799620
658:Software
479:zero-sum
462:called "
368:76963800
282:Language
3717:Bibcode
3673:Science
3621:3780848
3598:Bibcode
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3490:4211448
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2514:Bibcode
2420:Bibcode
2412:Science
2398:: 12–21
2301:2058440
2273:Bibcode
2265:Science
2249:1316190
2221:Bibcode
2213:Science
2196:6 March
2155:Science
2105:Bibcode
2070:6032103
2042:Bibcode
2034:Science
1990:: 5–6,
1941:7466396
1921:Bibcode
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1342:Bibcode
991:Science
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862:: 12–21
798:Bibcode
740:7466396
720:Bibcode
712:Science
668:Fortran
488:greater
285:English
187:may be
3835:Holism
3782:
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3709:Nature
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691:Python
677:PRISON
672:online
483:cannot
381:302 14
272:Author
3733:S2CID
3697:S2CID
3661:S2CID
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908:(PDF)
708:(PDF)
340:Pages
290:Genre
3780:ISBN
3751:: D3
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