The Evolution of Cooperation

Prisoner's Dilemma basic

The evolution of cooperation‘ is the title of a 1981 paper by political scientist Robert Axelrod and evolutionary biologist W. D. Hamilton on the emergence and persistence of cooperation (also known as cooperation theory) as elucidated by application of game theory.

Three years later, Axelrod discussed the topic at length in a similarly titled book. He was interested in how game theory and computer modeling were illuminating certain aspects of moral and political philosophy, particularly the role of individuals in groups, the ‘biology of selfishness and altruism,’ and the evolutionary advantages of cooperation.

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 the Royal Air Force’s hunt for submarines in the Bay of Biscay. 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’ depended not only on the number of submarines present, but also on the number of eyes looking; i.e., patrol density. 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.

The mathematical analysis of human behavior received scholarly attention in 1944 with mathematician John von Neumann and economist Oskar Morgenstern’s ‘Theory of Games and Economic Behavior’ on the use of game theory for developing and analyzing optimal strategies for military and other uses. It came to popular attention with the publication of John William’s ‘The Compleat Strategyst,’ an exposition of game theory in lay terms.

However, 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 for mutual gain, but each also takes a risk of being suckered. The game was (invented around 1950 by mathematicians Merrill Flood and Melvin Dresher) takes its name from the following scenario: you and a criminal associate have been busted. Fortunately for you, most of the evidence was shredded, so you are 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.

To cooperate, or not cooperate? This simple question (and the implicit question of whether to trust, or not), expressed in an extremely simple game, is a crucial issue across a broad range of life. For example, fig wasps collectively limit the eggs they lay in fig trees (otherwise, the trees would suffer). But why shouldn’t any one fig wasp cheat and leave a few more eggs than her rivals? At the level of human society, why shouldn’t each of the villagers that share a common but finite resource try to exploit it more than the others (moral hazard / tragedy of the commons) Yet, fig wasps and villagers all cooperate. It has been a vexatious problem in evolutionary studies to explain how such cooperation should evolve, let alone persist, in a world of self-maximizing egoists.

Charles Darwin’s theory of how evolution works (‘By Means of Natural Selection’) is explicitly competitive (‘survival of the fittest’), Malthusian (‘struggle for existence’), and even gladiatorial (‘nature, red in tooth and claw’). Species are pitted against species for shared resources; similar species with similar needs and niches even more so, and individuals within species most of all. All this comes down to one factor: out-competing all rivals and predators in producing progeny. Darwin’s explanation of how preferential survival of the slightest benefits can lead to advanced forms is the most important explanatory principle in biology, and is relevant in many other fields as well. Such success has reinforced notions that life is in all respects a war of each against all, where every individual has to look out for himself, that your gain is my loss.

In such a struggle for existence, altruism (voluntarily yielding a benefit to a non-relative) and even cooperation (working with another for a mutual benefit) seem so antithetical to self-interest as to be the very kind of behavior that should be selected against. Yet cooperation and seemingly even altruism have evolved and persist, and naturalists have been hard pressed to explain why.

The popularity of the evolution of cooperation – the reason it is not an obscure technical issue of interest to only a small number of specialists – is in part because it mirrors a larger issue where the realms of political philosophy, ethics, and biology intersect: 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) declaim that the world is an inherently competitive ‘dog eat dog’ jungle, where every individual has to look out for himself. Ayn Rand damned ‘altruism’ and declared selfishness a virtue. What she and other social Darwinists read into the theory was a scientific justification for their social and economic views (such as poverty being a natural condition and social reform an unnatural meddling).

Such views of evolution, competition, and the survival of the fittest are explicit in the ethos of modern capitalism, as epitomized by industrialist Andrew Carnegie in ‘The Gospel of Wealth’ (1889): ‘[W]hile the law [of competition] may be sometimes hard for the individual, it is best for the race, because it ensures the survival of the fittest in every department. We accept and welcome, therefore, as conditions to which we must accommodate ourselves, great inequality of environment; the concentration of business, industrial and commercial, in the hands of the few; and the law of competition between these, as being not only beneficial, but essential to the future progress of the race.’

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’ (1651): ‘[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….’ He added, ‘[C]ovenants without the sword are but words….’

Jean Jacques Rousseau wrote in ‘The Social Contract’ (1762): ‘[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?’ And, ‘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….’

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.’

The original role of government is to provide the coercive power to enforce the social contract (and in commercial societies, contracts and covenants generally). Where government does not exist or cannot reach it is often deemed the role of religion to promote prosocial and moral behavior, but this tends to depend on threats of hellfire (what Hobbes called ‘the terror of some power’); such inducements seem more mystical than rational, and philosophers have been hard-pressed to explain why self-interest should yield to morality, why there should be any duty to be ‘good.’

Yet cooperation, and even altruism and morality, are prevalent, even in the absence of coercion, even though it seems that a properly self-regarding individual should reject all such social strictures and limitations. As early as 1890 Russian naturalist Petr Kropotkin observed that the species that survived were where the individuals cooperated, that ‘mutual aid’ (cooperation) was found at all levels of existence. 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 – and even microbes (see microbial cooperation) were cooperating.

A possible explanation of altruism is provided by the theory of group selection (first suggested by Darwin himself while grappling with issue of social insects) which argues that natural selection can act on groups: groups that are more successful – for any reason, including learned behaviors – will benefit the individuals of the group, even if they are not related. It has had a powerful appeal, but has not been fully persuasive, in part because of difficulties regarding cheaters that participate in the group without contributing.

Another explanation is provided by the genetic kinship theory of evolutionary biologist William D. Hamilton: ‘if a gene causes an individual to help other individuals that carry copies of that gene, then the gene has a net benefit even with the sacrifice of a few individuals. The classic example is the social insects, where the workers – which are sterile, and therefore incapable of passing on their genes – benefit the queen, who is essentially passing on copies of ‘their’ genes. This is further elaborated in the ‘selfish gene’ theory of Richard Dawkins, that the unit of evolution is not the individual organism, but the gene. (As stated by Wilson: ‘the organism is only DNA’s way of making more DNA.’) However, kinship selection works only where the individuals involved are closely related; it fails to explain the presence of altruism and cooperation between unrelated individuals, particularly across species.

In a 1971 paper, sociobiologist Robert Trivers demonstrated how reciprocal altruism can evolve between unrelated individuals, even between individuals of entirely different species. And the relationship of the individuals involved is exactly analogous to the situation in a certain form of the Prisoner’s Dilemma. The key is that in the iterated Prisoner’s Dilemma, or IPD, both parties can benefit from the exchange of many seemingly altruistic acts. As Trivers says, it ‘take[s] the altruism out of altruism.’ The Randian premise that self-interest is paramount is largely unchallenged, but turned on its head by recognition of a broader, more profound view of what constitutes self-interest.

It does not matter why the individuals cooperate. The individuals may be prompted to the exchange of ‘altruistic’ acts by entirely different genes, or no genes in particular, but both individuals (and their genomes) can benefit simply on the basis of a shared exchange. In particular, ‘the benefits of human altruism are to be seen as coming directly from reciprocity – not indirectly through non-altruistic group benefits.’ Trivers’ theory is very powerful. Not only can it replace group selection, it also predicts various observed behavior, including moralistic aggression, gratitude and sympathy, guilt and reparative altruism, and development of abilities to detect and discriminate against subtle cheaters.

The benefits of such reciprocal altruism was dramatically demonstrated by a pair of tournaments held by Robert Axelrod around 1980. 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 mathematical psychologist 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 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 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 [and] by promoting the mutual interest rather than by exploiting the other’s weakness.’

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 to both retaliation and forgiveness. When the other player defects, a nice strategy must immediately be provoked into retaliatory defection. 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.

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. But real life is not zero-sum. Our best prospects are usually in cooperative efforts. In fact, TFT cannot 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 greater than the other player’s.

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.’ Against TFT (and ‘nice’ strategies generally) one can do no better than to simply cooperate. Axelrod calls this clarity (or ‘don’t be too clever’).

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 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 astounding: 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.

In summary, success in an evolutionary ‘game’ correlated with the following characteristics: Be nice (cooperate, never be the first to defect), Be provocable (return defection for defection, cooperation for cooperation), Don’t be envious (be fair with your partner), and Don’t be too clever (don’t try to be tricky).

These lessons apply in environments that support cooperation, but whether cooperation is supported at all depends crucially on the probability that the players will meet again, called the discount parameter or, poetically, the shadow of the future. When 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, 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.

Even when the discount parameter 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 if 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’). 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.

Axelrod wrote a subsequent book in 1997, ‘The Complexity of Cooperation,’ which he considers a sequel to ‘The Evolution of Cooperation.’ 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 Public Goods game (subjects secretly choose how many of their private tokens to put into a public pot) and Ultimatum game (two players decide how to divide a sum of money that is given to them) to explore deep-seated notions of fair play. It has also been used to challenge the rational and self-regarding ‘economic man’ model of economics, and as a basis for replacing Darwinian sexual selection theory with a theory of social selection.

Nice strategies are better able to invade if they have social structures or other means of increasing their interactions. In a later paper, Axelrod and computer scientists Rick Riolo 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 green beard).

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, Professor of Biology and Mathematics at Harvard University Martin Nowak and Viennese mathematician 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 it cooperates; if S or T it defects.

In a 2006 paper Nowak listed mechanisms by which natural selection can lead to cooperation. 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 nearby neighbors (it is essentially a virtual group); and Group selection 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. 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.

In small populations 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 social networks which exhibit some of the properties observed in empirical networks.


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