The Evolution of Cooperation

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The Evolution of Cooperation generally refers to:

This article is an introduction to how game theory and computer modeling are illuminating certain aspects of moral and political philosophy, particularly the role of individuals in groups, the "biology of selfishness and altruism"[2], and how cooperation can be evolutionarily advantageous.

Contents

[edit] Operations Research

The idea that human behavior can be usefully analyzed mathematically gained great credibility following the application of operations research in World War II to improve military operations. One famous example involved how the Royal Air Force hunted submarines in the Bay of Biscay.[3] It had seemed to make sense to patrol the areas where submarines were most frequently seen. Then it was pointed out that "seeing the most submarines" was also a function of patrol density – i.e., of the number of eyes looking. Making an allowance for patrol density showed that patrols were more efficient – that is, found more submarines per patrol – in other areas. Making appropriate adjustments increased the overall effectiveness.

[edit] Game Theory

Accounts of the success of operations research during the war, publication in 1944 of Von Neumann and Morgenstern's Theory of Games and Economic Behavior (Von Neumann & Morgenstern 1944) on the use of game theory for developing and analyzing optimal strategies for military and other uses, and publication of John William's The Compleat Strategyst, a popular exposition of game theory[4], led to a greater appreciation of mathematical analysis of human behavior.

But game theory had a little crisis: it could not find a strategy for a simple game called "The Prisoner's Dilemma" (PD) where two players have the option to cooperate together for mutual gain, but each also takes a risk of being suckered.

[edit] Prisoner's Dilemma

The Prisoner's Dilemma game (invented around 1950 by Merrill Flood and Melvin Dresher[5]) is named for this scenario: you and a criminal associate have been busted. Fortunately, most of the evidence was shredded, so you're facing only a year in prison. But the prosecutor wants to nail someone, so he offers you a deal: if you squeal on your associate – which will result in his getting a five year stretch – the prosecutor will see that six months is taken off of your sentence. Which sounds good, until you learn your associate is being offered the same deal – which would get you five years.

So what do you do? The best that you and your associate can do together is to not squeal – that is, to cooperate (with each other, not the prosecutor!) in a mutual bond of silence, and do your year. But wait: if your associate cooperates (that sucker!), can you do better by squealing ("defecting") to get that six month reduction? It's tempting, but then he's also tempted. And if you both squeal, oh, no, it's four and half years each. So perhaps you should cooperate – but wait, that's being a sucker yourself, as your associate will undoubtedly defect, and you won't even get the six months off. So what is the best strategy to minimize your incarceration? (Aside from going straight in the first place.)

Technically, the Prisoner's Dilemma is any two-person "game" where the payoffs are ranked in a certain way. If the payoff ("reward") for mutual cooperation is R, for mutual defection is P, the sucker gets only S, and the temptation payoff (provided the other player is suckered into cooperating) is T, then the payoffs need to be ordered T > R > P > S, and satisfy R > (T+S)/2. (pp. 8–10, 206–207).[6]

[edit] Social Darwinism vs. Mutual Aid

The popularity of this issue is in part because it mirrors a larger issue where the realms of political philosophy, ethics, and biology cross: the ancient issue of individual interests versus group interests. On one hand, the so-called "Social Darwinians" (roughly, those who would use the "survival of the fittest" of Darwinian evolution to justify the cutthroat competitiveness of laissez-faire capitalism[7]) declaim that the world is an inherently competitive "dog eat dog" jungle, where every individual has to look out for himself. The philosopher Ayn Rand damned "altruism" and declared selfishness a virtue.[8] The Social Darwinists' view is derived from Charles Darwin's interpretation of evolution by natural selection, which is explicitly competitive ("survival of the fittest"), Malthusian ("struggle for existence"), even gladiatorial ("red in tooth and claw"), and permeated by the Victorian laissez faire ethos of Darwin and his disciples (such as T. H. Huxley and Herbert Spencer). What they read into the theory was then read out by Social Darwinians as scientific justification for their social and economic views (such as poverty being a natural condition and social reform an unnatural meddling).[9]

As early as 1902 the Russian naturalist (and anarchist) Petr Kropotkin had complained: "They raised the 'pitiless' struggle for personal advantage to the height of a biological principle, which man must submit to as well, under the menace of otherwise succumbing in a world based on mutual extermination."[10] Kropotkin argued that mutual aid was as much a factor in evolution as the "struggle for existence", a position now reached by the theory of cooperation. (See Stephen Jay Gould's essay "Kropotkin Was No Crackpot" (Gould 1997). Why Kropotkin's view languished, why the interpretation of Darwinian theory developed the way it did, and the various political ramifications are interesting topics worth further study, but beyond the scope of this article.)

[edit] The Social Contract

On the other hand, other philosophers have long observed that cooperation in the form of a "social contract" is necessary for human society, but saw no way of attaining that short of a coercive authority.

As Thomas Hobbes wrote in Leviathan:

[T]here must be some coercive power to compel men equally to the performance of their covenants by the terror of some punishment greater than the benefit they expect by the breach of their covenant.... (Hobbes 1651, p. 120)

[C]ovenants without the sword are but words.... (Hobbes 1651, p. 1139)

And Jean Jacques Rosseau in The Social Contract:

[The social contract] can arise only where several persons come together: but, as the force and liberty of each man are the chief instruments of his self-preservation, how can he pledge them without harming his own interests, and neglecting the care he owes himself? (Rousseau 1762, p. 13)

In order then that the social compact may not be an empty formula, it tacitly includes the undertaking, which alone can give force to the rest, that whoever refuses to obey the general will shall be compelled to do so by the whole body. This means nothing less than that he will be forced to be free.... (Rousseau 1762, p. 18)

Even Herman Melville, in Moby-Dick, has the cannibal harpooner Queequeg explain why he has saved the life of someone who had been jeering him as so:

"It's a mutual, joint-stock world, in all meridians. We cannibals must help these Christians." (Melville 1851, p. 96)

Although the Social Darwinians claimed that altruism and even cooperation were unrealistic, by the 1960s biologists and zoologists were noting many instances in the real "jungle" where real animals – presumably unfettered by conscience and not corrupted by altruistic liberals – were cooperating.[11] So is cooperation necessary? Is it possible? Is it evil? Is it as intractable as the Prisoner's Dilemma suggests?

[edit] Altruism and cooperation

Altruism can be defined as "the willingness to sacrifice oneself for others"[12], to voluntarily take a loss, or a risk of a loss. Although altruism – such as risking one's own life to save another, or going to war – has been glorified since the dawn of human history (and probably before), what does the altruist get out of it? In evolutionary terms, survival of a self-sacrificing "altruist gene" – not to be confused with some kind of gene to con others into self-sacrifice – would seem impossible.

One approach – that of sociobiology – considers survival as acting on groups (individuals are expendible); it has not been fully persuasive.[13]

Another approach explains altruism as more apparent than real, due to indirect or hidden benefits; in particular, benefits to near kin, who share many genes with the altruist, might serve to advance an "altruist gene". This upsets the definition; it "take[s] the altruism out of altruism".(Trivers 1971) So what are we examining: altruism? Or the appearance of altruism?

In a like manner, cooperation and other prosocial behavior, once deemed altruistic, can now be seen as solidly based on a well-considered self-regard. The Randian premise that puts self-interest paramount is largely unchallenged. What has changed is the recognition of a broader, more profound view of what constitutes self-interest.

A partial explanation for the persistence of cooperation and altruism in the wild was provided by the genetic kinship theory of William D. Hamilton.[14] The key idea is that the unit of survival is not the individual – no one one lives forever – but the genome. Altruism – taking a loss for the benefit of another – can be evolutionarily advantageous because the loss of a few progeny could advance other progeny who are carrying the same genes. However, this works only where the individuals involved are closely related; it fails to explain how unrelated individuals might benefit from cooperation.

Alternately, the reciprocity theory of Robert Trivers (Trivers 1971) suggested a basis for cooperation between unrelated individuals, but simple reciprocity seemed to be as intractable as the PD. However, it turns out that the iterated Prisoner's Dilemma, or IPD, is amenable to analysis. And it shows that, where there is a repeated interaction, cooperation arises naturally because the individuals involved can obtain a greater benefit. This was dramatically demonstrated by a pair of tournaments held by Robert Axelrod around 1980.

[edit] Axelrod's Tournaments

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 Prisoner's Dilemma game, and scored on the total points accumulated through the tournament. The winner was a very simple strategy submitted by Anatol Rapoport called "TIT FOR TAT" (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 held to see if anyone could find a better strategy. TIT FOR TAT won again. Axelrod analyzed the results, and made some interesting discoveries about the nature of cooperation, which he describes in his book

In both the actual tournaments and various simulations the best performing strategies were "nice" (p. 113[15]): 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 for a few points generally could not do as well as nice strategies working together. There is a profound lesson here: TFT (and other "nice" strategies generally) "won, not by doing better than the other player, but by eliciting cooperation [and] by promoting the mutual interest rather than by exploiting the other's weakness." (p. 130)

The lesson rapidly broadens: Most of the games that game theory had heretofore investigated are "zero-sum" – that is, the total rewards are fixed, and a player does well only at the expense of other players – and the adage "survival of the fittest" implies that one player is a winner and the other a loser. But real life is not zero-sum. Although our culture glorifies heroic individualism, our best prospects are usually in cooperative efforts. In fact, TFT cannot score higher than its partner; it won the tournaments by consistently scoring a strong second-place (p. 112). Axelrod summarizes this as don't be envious (pp. 110–113); in other words, don't strive for a payoff greater than the other player's (p. 25).

While rightists could well take a lesson here that being "nice" can be beneficial, leftists should note that nice can lead to being suckered. To obtain the benefit – or avoid exploitation – it is necessary to understand the requisite conditions. In particular: it is necessary to be provocable to both retaliation and forgiveness. That is, when the other player defects, a nice strategy must immediately be provoked into retaliatory defection (pp. 62, 211).[16] The same goes 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 (p. 186)

The fourth property of successful strategies is clarity. Or: don't be too clever (p. 120+).

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 TIT FOR TAT, but generally they do poorly. "A common problem with these rules is that they used complex methods of making inferences about the other player [strategy] – and these inferences were wrong." (p. 120) Against TFT (and "nice" strategies generally) one can do no better than to simply cooperate (pp. 47, 118).

Axelrod also did an "ecological" tournament, where the prevalence of each type of strategy in 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 (pp. 48–53).

Axelrod is not without critics. Binmore (1998b) says Axelrod's simlulation data is "woefully inadequate" and dependent on particular conditions; he decries inadequate consideration of game theory and the popularization of TFT as general model for human behavior.

[edit] Foundation of reciprocal cooperation

The lessons described above apply in environments that support cooperation, but whether cooperation is supported at all depends crucially on the probability (called ω (omega)) that the players will meet again (p. 13), also called the discount parameter or, poetically, the shadow of the future. When ω is low – 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 a single exploitation (which is all that a strategy like TFT will tolerate).

Curiously, rationality and deliberate choice are not necessary, nor trust nor even consciousness (pp. 18, 174), 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 "discovered" a beneficial pattern both parties respond to it by continuing the conditions that maintain it.

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 player's strategy (p. 174).

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 strategy can get established by isolated individuals; cooperation is strictly a sucker bet. (The "futility of isolated revolt", p. 150.) 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 (pp. 63–68, 99).

[edit] Subsequent work

In 1984 Axelrod estimated that there were "hundreds of articles on the Prisoner's Dilemma cited in Psychological Abstracts".[17] Since then he has estimated that citations to The Evolution of Cooperation alone "are now growing at the rate of over 300 per year".[18] To fully review this literature is infeasible. What follows are therefore only a few selected highlights.

Axelrod has a subsequent book, The Complexity of Cooperation,[19] which he considers a sequel to The Evolution of Cooperation. Other work on the evolution of cooperation has expanded to cover prosocial behavior generally,[20] and in religion,[21] the promotion of conformity,[22] other mechanisms for generating cooperation,[23] the IPD under different conditions and assumptions,[24] and the use of other games such as the Public Goods and Ultimatum games to explore deep-seated notions of fairness and fair play.[25] It has also been used to challenge the rational and self-regarding "economic man" model of economics,[26] and as a basis for replacing Darwinian sexual selection theory with a theory of social selection.[27]

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 Rick Riolo and Michael Cohen[28] use computer simulations to show cooperation rising among agents who have negligible chance of future encounters but can recognize similarity of an arbitrary characteristic.

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.[29] In 1992 Martin Nowak and Karl Sigmund demonstrated a strategy called Pavlov (or "win–stay, lose–shift") that does better in these circumstances.[30] 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.

In a 2006 paper Nowak listed five mechanisms by which natural selection can lead to cooperation.[31] In addition to kin selection and direct reciprocity, he shows that:

  • 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 partners.
  • Network reciprocity relies on geographical or social factors to increase the interactions with nearer neighbors; it is essentially a virtual group.
  • Group selection[32] assumes that groups with cooperators (even altruists) will be more successful as a whole, and this will tend to benefit all members.

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.[33] Other work has shown that while 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.[34]

And there is the very intriguing paper "The Coevolution of Parochial Altruism and War" by Jung-Kyoo Choi and Samuel Bowles. From their summary:

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 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.... [Neither] would have been viable singly, but by promoting group conflict they could have evolved jointly. (Choi & Bowles 2007)

They do not 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.

[edit] Conclusion

When Richard Dawkins set out to "examine the biology of selfishness and altruism" in The Selfish Gene, he reinterpreted basis of evolution, and therefore of altruism. He was "not advocating a morality based on evolution",[35] and even felt that "we must teach our children altruism, for we cannot expect it to be part of their biological nature."[36] But Trivers (1971) had shown that altruism (cooperation) could be based on reciprocity of behavior, John Maynard Smith[37] was showing that behavior could be subject to evolution and Axelrod's dramatic results showed that in a very simple game the conditions for survival (be "nice", promote the mutual interest) seem to be the essence of morality. While this does not yet amount to a science of morality, the game theoretic approach has established that cooperation can be individually profitable and evolutionarily viable, and has clarified the requisite conditions. Extensions of this work to morality[38] and the social contract[39] may yet resolve the old issue of individual interests versus group interests.

[edit] Recommended Reading

[edit] Notes

  1. ^ Axelrod's book was summarized in Douglas Hofstadter's May 1983 "Metamagical Themas" column in Scientific American (Hofstadter 1983) (reprinted in his book (Hofstadter 1985); see also Richard Dawkin's summary in the second edition of The Selfish Gene ((Dawkins 1989), ch. 12.)
  2. ^ Dawkins 1989.
  3. ^ Morse & Kimball 1951, 1956.
  4. ^ Williams 1954, 1966
  5. ^ Axelrod 1984, p. 216 n. 2; Poundstone 1992.
  6. ^ All unattributed page numbers are to "The Evolution of Cooperation" (Axelrod 1984).
  7. ^ Bowler 1984, pp. 94–99, 269–70.
  8. ^ Rand 1961.
  9. ^ Bowler 1984, pp. 94–99
  10. ^ Kropotkin 1902, pp. 4
  11. ^ Axelrod 1984, pp. 90; Trivers 1971.
  12. ^ Bowler 1984, p. 215.
  13. ^ Trivers 1971, p. 48; Bowler 1984, p. 312; Dawkins 198, pp. 7–10, 287, ch. 7 generally.
  14. ^ Hamilton 1963, 1964; Dawkins 1989.
  15. ^ Partial references are to Axelrod (1984).
  16. ^ Bertold Brecht's "Good Woman of Setzuan" (Brecht 1947) could not survive without the occasional visit of the cousin. An intriguing question is why she cannot apply the necessary correctives herself.
  17. ^ Axelrod 1984, pp. 28.
  18. ^ Axelrod 1984, pp. 3.
  19. ^ Axelrod 1997.
  20. ^ Boyd 2006; Bowles 2006.
  21. ^ Norenzayan & Shariff 2008.
  22. ^ Bowles 2003.
  23. ^ Nowak 2006.
  24. ^ Axelrod & Dion 1988.
  25. ^ Nowak, Page & Sigmund 2000; Sigmund, Fehr & Nowak 2002.
  26. ^ Camerer & Feher 2006.
  27. ^ Roughgarden, Oishi & Akcay 2006.
  28. ^ Axelrod, Riolo & Cohen 2001.
  29. ^ Axelrod (1984, pp. 136–138) has some interesting comments on the need to suppress universal cooperators. See also a similar theme in Piers Anthony's novel Macroscope.
  30. ^ Nowak & Sigmund 1992; see also Milinski 1993.
  31. ^ Nowak 2006.
  32. ^ Here group selection is not a form of evolution, which is problematical (see Dawkins (1989), ch. 7), but a mechanism for evolving cooperation.
  33. ^ Hauert & et.al. 2007.
  34. ^ Gurek, Irienbush & Rockenback 2006.
  35. ^ Dawkins 1989, p. 2.
  36. ^ Dawkins 1989, p. 139.
  37. ^ Maynard Smith 1976, 1978, 1982.
  38. ^ Gauthier 1986.
  39. ^ Kavka 1986; Binmore 1994, 1998a, 2004.

[edit] References

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.

  • Axelrod, Robert (1997), The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration, Princeton University Press 
  • Axelrod, Robert (2006), The Evolution of Cooperation (Revised ed.), Basic Books 
  • Binmore, Kenneth G. (1994), Game Theory and the Social Contract: Vol. 1, Playing Fair, MIT Press 
  • Binmore, Kenneth G. (1998a), Game Theory and the Social Contract: Vol. 2, Just Playing, MIT Press 
  • Bowler, Peter J. (1984), Evolution: The History of an Idea, Univ. of California Press, ISBN 0-520-04880-3 
  • Brecht, Bertolt (1947), The Good Woman of Setzuan 
  • Dawkins, Richard ([1976] 1989), The Selfish Gene (2nd ed.), Oxford Univ. Press, ISBN 0-19-286092-5 
  • Gauthier, David (1986), Morals by agreement, Oxford Univ. Press 
  • Hamilton, William D. (1964), "The Genetical Evolution of Social Behavior", J. of Theoretical Biology 7: 1–16, 17–52 
  • Hobbes, Thomas ([1651] 1958), Leviathan, Bobbs-Merrill [and others] 
  • Hofstadter, Douglas R. (May, 1983), "Metamagical Themas: Computer Tournaments of the Prisoner's Dilemma Suggest How Cooperation Evolves", Scientific American 248: 16–26 
  • Hofstadter, Douglas R. (1985), "The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation", Metamagical Themas: Questing for the Essence of Mind and Pattern, Basic Books, pp. 715–730, ISBN 0-465-04540-5 
  • Kavka, Gregory S. (1986), Hobbesian moral and political theory, Princeton Univ. Press 
  • Kropotkin, Petr (1902, 1914), Mutual Aid: A Factor in Evolution 
  • Maynard Smith, John (1976), "Evolution and the Theory of Games", American Scientist 61: 41–45 
  • Maynard Smith, John (September 1978), "The Evolution of Behavior", Scientific American 239: 176–92 
  • Maynard Smith, John (1982), Evolution and the Theory of Games, Cambridge Univ. Press 
  • Melville, Herman ([1851] 1977), Moby-Dick, Bobbs-Merrill [and others] 
  • Milinski, Manfred (1 July 1993), "News and Views: Cooperation Wins and Stays", Nature 364: 12–13, doi:10.1038/364012a0 
  • Morse, Phillip M.; Kimball, George E. (1951), Methods of Operations Research 
  • Morse, Phillip M.; Kimball, George E. (1956), "How to Hunt a Submarine", The World of Mathematics, 4, Simon and Schuster, pp. 2160–79 
  • Poundstone, William (1992), Prisoner's Dilemma: John von Neumann, Game Theory and the Puzzle of the Bomb, Anchor Books, ISBN 0-385-41580-X 
  • Rand, Ayn (1961), The Virtue of Selfishness: A New Concept of Egoism, The New American Library 
  • Rapoport, Anatol; Chammah, Albert M. (1965), Prisoner's Dilemma, Univ. of Michigan Press 
  • Rousseau, Jean Jacques ([1762] 1950), The Social Contract, E. P. Dutton & Co. [and others] 
  • Sanfey, Alan G. (26 Oct. 2007), "Social Decision-Making: Insights from Game Theory and Neuroscience", Science 318: 598–602, doi:10.1126/science.1142996 
  • Trivers, Robert L. (March 1971), "The Evolution of Reciprocal Altruism", Quarterly Review of Biology 46: 35–57 
  • Von Neumann, John; Morgenstern, Oskar (1944), Theory of Games and Economic Behavior, Princeton Univ. Press 
  • Williams, John D. (1954), The Compleat Strategyst, RAND Corp. 
  • Williams, John D. (1966), The Compleat Strategyst: being a primer on the theory of games of strategy (2nd ed.), McGraw-Hill Book Co. 
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