Group-size diversity in public goods games

Public goods games are models of social dilemmas where cooperators pay a cost for the production of a public good while defectors free ride on the contributions of cooperators. In the traditional framework of evolutionary game theory, the payoffs of cooperators and defectors result from interactions in groups formed by binomial sampling from an infinite population. Despite empirical evidence showing that group-size distributions in nature are highly heterogeneous, most models of social evolution assume that the group size is constant. In this article, I remove this assumption and explore the effects of having random group sizes on the evolutionary dynamics of public goods games. By a straightforward application of Jensen's inequality, I show that the outcome of general nonlinear public goods games depends not only on the average group size but also on the variance of the group-size distribution. This general result is illustrated with two nonlinear public goods games (the public goods game with discounting or synergy and the N-person volunteer's dilemma) and three different group-size distributions (Poisson, geometric, and Waring). The results suggest that failing to acknowledge the natural variation of group sizes can lead to an underestimation of the actual level of cooperation exhibited in evolving populations.     

Runaway selection for cooperation and strict-and-severe punishment

Punishing defectors is an important means of stabilizing cooperation. When levels of cooperation and punishment are continuous, individuals must employ suitable social standards for defining defectors and for determining punishment levels. Here we investigate the evolution of a social reaction norm, or psychological response function, for determining the punishment level meted out by individuals in dependence on the cooperation level exhibited by their neighbors in a lattice-structured population. We find that (1) cooperation and punishment can undergo runaway selection, with evolution towards enhanced cooperation and an ever more demanding punishment reaction norm mutually reinforcing each other; (2) this mechanism works best when punishment is strict, so that ambiguities in defining defectors are small; (3) when the strictness of punishment can adapt jointly with the threshold and severity of punishment, evolution favors the strict-and-severe punishment of individuals who offer slightly less than average cooperation levels; (4) strict-and-severe punishment naturally evolves and leads to much enhanced cooperation when cooperation without punishment would be weak and neither cooperation nor punishment are too costly; and (5) such evolutionary dynamics enable the bootstrapping of cooperation and punishment, through which defectors who never punish gradually and steadily evolve into cooperators who punish those they define as defectors.     

The evolution of punishment and apology: an iterated prisoner's dilemma model

Recently, behaviors that seem to function as punishment or apology have been reported among non-human primates as well as humans. Such behaviors appear to play an important role in maintaining cooperation between individuals. Therefore, the evolution of these behaviors should be examined from the viewpoint of the evolution of cooperation. The iterated prisoner's dilemma (IPD) game is generally considered to be a standard model for the evolution of cooperation. In the present study, strategies accompanied by punishment-like attacks or apology-like behavior were introduced into the common IPD simulation. Punishment and apology were represented by the P signal and the AS signal given immediately after defection. A strategy with the P and AS signals, named the pPAS strategy, was proved to be an evolutionarily stable strategy under certain conditions. Numerical simulations were carried out according to different assigned values of the costs of punishment and apology. The simulations showed that pPAS could dominate the population (1) when the cost of giving P is relatively small, (2) when the cost of receiving P is relatively large, or (3) when the cost of giving AS is relatively large. The relative cost of giving AS had the clearest effect on the success of pPAS. pPAS can dominate the population even when a dominance asymmetry of the costs between two players was introduced. The present results suggest the possible evolution of social behaviors like punishment or apology as a means of maintaining cooperation. This revised version was published online in November 2006 with corrections to the Cover Date.     

Punishing free riders: direct and indirect promotion of cooperation

Human cooperation in a large group of genetically unrelated people is an evolutionary puzzle. Despite its costly nature, cooperative behavior is commonly found in all human societies—a fact that has interested researchers from a wide range of disciplines, including biology, economics, and psychology, to name a few. Many behavioral experiments have demonstrated that cooperation within a group can be sustained when free riders are punished. We argue that punishment has both a direct effect and an indirect effect on promoting cooperation. The direct effect of punishment alters the consequences of cooperation and defection in such a way as to make a rational person prefer cooperation. The indirect effect of punishment promotes cooperation among conditional cooperators by providing the condition necessary for their cooperation (i.e., the expectation that other members will also cooperate). Here we present data from two one-shot n-person prisoner's dilemma games, demonstrating that the indirect effect of punishment complements the direct effect to increase cooperation in the game. Furthermore, we show that direct and indirect effects are robust across two forms of punishment technology: either when punishment is voluntarily provided by game players themselves or when it is exogenously provided by the experimenter.     

When Punishment Pays

Explaining cooperation in groups remains a key problem because reciprocity breaks down between more than two. Punishing individuals who contribute little provides a potential answer but changes the dilemma to why pay the costs of punishing which, like cooperation itself, provides a public good. Nevertheless, people are observed to punish others in behavioural economic games, posing a problem for existing theory which highlights the difficulty in explaining the spread and persistence of punishment. Here, I consider the apparent mismatch between theory and evidence and show by means of instructive analysis and simulation how much of the experimental evidence for punishment comes from scenarios in which punishers may expect to obtain a net benefit from punishing free-riders. In repeated games within groups, punishment works by imposing costs on defectors so that it pays them to switch to cooperating. Both punishers and non-punishers then benefit from the resulting increase in cooperation, hence investing in punishment can constitute a social dilemma. However, I show the conditions in which the benefits of increased cooperation are so great that they more than offset the costs of punishing, thereby removing the temptation to free-ride on others'' investments and making punishment explicable in terms of direct self-interest. Crucially, this is because of the leveraging effect imposed in typical studies whereby people can pay a small cost to inflict a heavy loss on a punished individual. In contrast to previous models suggesting punishment is disadvantaged when rare, I show it can invade until it comes into a producer-scrounger equilibrium with non-punishers. I conclude that adding punishment to an iterated public goods game can solve the problem of achieving cooperation by removing the social dilemma.     

Towards a Biopsychological Understanding of Costly Punishment: The Role of Basal Cortisol

Recent findings have documented a negative relation of basal endogenous cortisol and aggression after a provocation (i.e., reactive aggression) in humans. We build on these findings and investigated the relation of endogenous cortisol and reactive aggression in a social dilemma situation, that is, costly punishment of individuals who did not appropriately contribute to a common group project. Specifically, we predicted that basal cortisol is negatively related to costly punishment of uncooperative individuals. In the present study, basal cortisol was assessed prior to a public goods game with the option to punish other group members. In line with previous research on reactive aggression and basal cortisol, we found that basal cortisol was indeed negatively related to costly punishment. The findings are important for understanding costly punishment because this tendency has been documented as a possible basis for the evolution of cooperation.     

The economics of altruistic punishment and the maintenance of cooperation

Explaining the evolution and maintenance of cooperation among unrelated individuals is one of the fundamental problems in biology and the social sciences. Recent findings suggest that altruistic punishment is an important mechanism maintaining cooperation among humans. We experimentally explore the boundaries of altruistic punishment to maintain cooperation by varying both the cost and the impact of punishment, using an exceptionally extensive subject pool. Our results show that cooperation is only maintained if conditions for altruistic punishment are relatively favourable: low cost for the punisher and high impact on the punished. Our results indicate that punishment is strongly governed by its cost-to-impact ratio and that its effect on cooperation can be pinned down to one single variable: the threshold level of free-riding that goes unpunished. Additionally, actual pay-offs are the lowest when altruistic punishment maintains cooperation, because the pay-off destroyed through punishment exceeds the gains from increased cooperation. Our results are consistent with the interpretation that punishment decisions come from an amalgam of emotional response and cognitive cost-impact analysis and suggest that altruistic punishment alone can hardly maintain cooperation under multi-level natural selection. Uncovering the workings of altruistic punishment as has been done here is important because it helps predicting under which conditions altruistic punishment is expected to maintain cooperation.     

The evolution of punishment through reputation

Punishment of non-cooperators has been observed to promote cooperation. Such punishment is an evolutionary puzzle because it is costly to the punisher while beneficial to others, for example, through increased social cohesion. Recent studies have concluded that punishing strategies usually pay less than some non-punishing strategies. These findings suggest that punishment could not have directly evolved to promote cooperation. However, while it is well established that reputation plays a key role in human cooperation, the simple threat from a reputation of being a punisher may not have been sufficiently explored yet in order to explain the evolution of costly punishment. Here, we first show analytically that punishment can lead to long-term benefits if it influences one''s reputation and thereby makes the punisher more likely to receive help in future interactions. Then, in computer simulations, we incorporate up to 40 more complex strategies that use different kinds of reputations (e.g. from generous actions), or strategies that not only include punitive behaviours directed towards defectors but also towards cooperators for example. Our findings demonstrate that punishment can directly evolve through a simple reputation system. We conclude that reputation is crucial for the evolution of punishment by making a punisher more likely to receive help in future interactions, and that experiments investigating the beneficial effects of punishment in humans should include reputation as an explicit feature.     

The Effect of Power Asymmetries on Cooperation and Punishment in a Prisoner’s Dilemma Game

Recent work has suggested that punishment is detrimental because punishment provokes retaliation, not cooperation, resulting in lower overall payoffs. These findings may stem from the unrealistic assumption that all players are equal: in reality individuals are expected to vary in the power with which they can punish defectors. Here, we allowed strong players to interact with weak players in an iterated prisoner''s dilemma game with punishment. Defecting players were most likely to switch to cooperation if the partner cooperated: adding punishment yielded no additional benefit and, under some circumstances, increased the chance that the partner would both defect and retaliate against the punisher. Our findings show that, in a two-player game, cooperation begets cooperation and that punishment does not seem to yield any additional benefits. Further work should explore whether strong punishers might prevail in multi-player games.     

Explaining the evolution of parochial punishment in humans

Humans usually favour members of their own group, ethnicity or culture (parochial cooperation), and punish out-group wrongdoers more harshly (parochial punishment). The evolution of parochial cooperation is mainly explained by intergroup conflict, as restricting cooperation to in-groups can provide a relative advantage during conflict. However, explanations for the evolution of parochial punishment are still lacking. It is unclear whether conflict can also explain parochial punishment, because conflict is expected to lead to full hostility towards out-groups, irrespective of their behaviour. Here, we use an agent-based simulation to explore which conditions favour the evolution of parochial third-party punishment. We show that when groups interact and then engage in conflict with each other, third-party punishment is not parochial but spiteful, and directed towards all out-groups. A parochial bias in punishment decisions evolves (i) without conflict, when groups compete against nature and enforcing cooperation requires many punitive actions, and (ii) with conflict, when groups come into conflict with a group other than one they previously interacted with. Our findings suggest that intergroup conflict does not always lead to parochial punishment, and that stable collaborative relations between groups is a key factor promoting third-party parochial punishment. Our findings also provide novel predictions on how punishment and intergroup conflict influence in-group bias in human societies.     

High strength-of-ties and low mobility enable the evolution of third-party punishment

As punishment can be essential to cooperation and norm maintenance but costly to the punisher, many evolutionary game-theoretic studies have explored how direct punishment can evolve in populations. Compared to direct punishment, in which an agent acts to punish another for an interaction in which both parties were involved, the evolution of third-party punishment (3PP) is even more puzzling, because the punishing agent itself was not involved in the original interaction. Despite significant empirical studies of 3PP, little is known about the conditions under which it can evolve. We find that punishment reputation is not, by itself, sufficient for the evolution of 3PP. Drawing on research streams in sociology and psychology, we implement a structured population model and show that high strength-of-ties and low mobility are critical for the evolution of responsible 3PP. Only in such settings of high social-structural constraint are punishers able to induce self-interested agents toward cooperation, making responsible 3PP ultimately beneficial to individuals as well as the collective. Our results illuminate the conditions under which 3PP is evolutionarily adaptive in populations. Responsible 3PP can evolve and induce cooperation in cases where other mechanisms alone fail to do so.     

Altruistic Punishment and Between-Group Competition

Collective action, or the large-scale cooperation in the pursuit of public goods, has been suggested to have evolved through cultural group selection. Previous research suggests that the costly punishment of group members who do not contribute to public goods plays an important role in the resolution of collective action dilemmas. If large-scale cooperation sustained by the punishment of defectors has evolved through the mechanism of cultural group selection, two implications regarding costly punishment follow: (1) that people are more willing to punish defecting group members in a situation of intergroup competition than in a single-group social dilemma game and (2) that levels of "perverse" punishment of cooperators are not affected by intergroup competition. We find confirmation for these hypotheses. However, we find that the effect of intergroup competition on the punishment of defectors is fully explained by the stronger conditionality of punishment on expected punishment levels in the competition condition.     

Anti-social punishment can prevent the co-evolution of punishment and cooperation

The evolution of cooperation is one of the great puzzles in evolutionary biology. Punishment has been suggested as one solution to this problem. Here punishment is generally defined as incurring a cost to inflict harm on a wrong-doer. In the presence of punishers, cooperators can gain higher payoffs than non-cooperators. Therefore cooperation may evolve as long as punishment is prevalent in the population. Theoretical models have revealed that spatial structure can favor the co-evolution of punishment and cooperation, by allowing individuals to only play and compete with those in their immediate neighborhood. However, those models have usually assumed that punishment is always targeted at non-cooperators. In light of recent empirical evidence of punishment targeted at cooperators, we relax this assumption and study the effect of so-called ‘anti-social punishment’. We find that evolution can favor anti-social punishment, and that when anti-social punishment is possible costly punishment no longer promotes cooperation. As there is no reason to assume that cooperators cannot be the target of punishment during evolution, our results demonstrate serious restrictions on the ability of costly punishment to allow the evolution of cooperation in spatially structured populations. Our results also help to make sense of the empirical observation that defectors will sometimes pay to punish cooperators.     

Individual heterogeneity and costly punishment: a volunteer's dilemma

Social control and the enforcement of social norms glue a society together. It has been shown theoretically and empirically that informal punishment of wrongdoers fosters cooperation in human groups. Most of this research has focused on voluntary and uncoordinated punishment carried out by individual group members. However, as punishment is costly, it is an open question as to why humans engage in the punishment of wrongdoers even in one-time-only encounters. While evolved punitive preferences have been advocated as proximate explanations for such behaviour, the strategic nature of the punishment situation has remained underexplored. It has been suggested to conceive of the punishment situation as a volunteer''s dilemma (VOD), where only one individual''s action is necessary and sufficient to punish the wrongdoer. Here, we show experimentally that implementing the punishment situation as a VOD sustains cooperation in an environment where punishers and non-punishers coexist. Moreover, we show that punishment-cost heterogeneity allows individuals to tacitly agree on only the strongest group member carrying out the punishment, thereby increasing the effectiveness and efficiency of social norm enforcement. Our results corroborate that costly peer punishment can be explained without assuming punitive preferences and show that centralized sanctioning institutions can emerge from arbitrary individual differences.     

Eco-evolutionary feedback and the invasion of cooperation in prisoner's dilemma games

Unveiling the origin and forms of cooperation in nature poses profound challenges in evolutionary ecology. The prisoner's dilemma game is an important metaphor for studying the evolution of cooperation. We here classified potential mechanisms for cooperation evolution into schemes of frequency- and density-dependent selection, and focused on the density-dependent selection in the ecological prisoner's dilemma games. We found that, although assortative encounter is still the necessary condition in ecological games for cooperation evolution, a harsh environment, indicated by a high mortality, can foster the invasion of cooperation. The Hamilton rule provides a fundamental condition for the evolution of cooperation by ensuring an enhanced relatedness between players in low-density populations. Incorporating ecological dynamics into evolutionary games opens up a much wider window for the evolution of cooperation, and exhibits a variety of complex behaviors of dynamics, such as limit and heteroclinic cycles. An alternative evolutionary, or rather succession, sequence was proposed that cooperation first appears in harsh environments, followed by the invasion of defection, which leads to a common catastrophe. The rise of cooperation (and altruism), thus, could be much easier in the density-dependent ecological games than in the classic frequency-dependent evolutionary games.     

Effect of the presence of empty sites on the evolution of cooperation by costly punishment in spatial games

Cooperation and spiteful behavior are still evolutionary puzzles. Costly punishment, for which the game payoff is the same as that of spiteful behavior, is one mechanism for promoting the evolution of cooperation. A spatially structured population facilitates the evolution of either cooperation or spite/punishment if cooperation is linked explicitly or implicitly with spite/punishment; a cooperator cooperates with another cooperator and punishes/spites the other type of player. Different updating rules in the evolutionary game produce different evolutionary outcomes: with one updating rule—the score-dependent viability model, in which a player dies with a probability inversely proportional to the game score and the resulting unoccupied site is colonized by one player chosen randomly—the evolution of spite/punishment is promoted more than with the other updating rule—the score-dependent fertility model, in which, after a player dies randomly, the site is colonized by a player with a higher game score. If the population has empty sites, spiteful players or punishers should have less chance to interact with others and then spite/punish others. Thus the presence of empty sites would affect the evolutionary dynamics of spite/punishment. Here, we investigated whether the presence of empty sites discourages the evolution of spite/punishment in both a lattice-structured population and a completely mixing population where players interact with others randomly, especially when the score-dependent viability model is adopted. In the lattice-structured population adopting this viability model, the presence of empty sites promoted the evolution of cooperation and did not reduce the effect of spite/punishment. In the completely mixing population, the presence of empty sites did not promote evolution of cooperation by punishment. The evolutionary dynamics of the score-dependent viability model with empty sites were close to those of the score-dependent fertility model.     

The volunteer's dilemma and the optimal size of a social group

If one or few individuals are enough to perform an action that produces a collective good and if this action has a cost, living in group can be beneficial because the cost can be shared with other individuals. Without coordination, however, the production of a collective good by the contribution of one or few individuals is inefficient and can be modelled as a volunteer's dilemma. In the volunteer's dilemma the individuals that pay the cost for the production of the collective good benefit from their action if nobody else volunteers, but the cost is wasted if too many individuals volunteer. Increasing group size reduces the need of volunteering for each member of the group; the overall benefit for the group, however, decreases too because the larger the group is, the less likely it is that the collective good is produced. This problem persists even with a high degree of relatedness between group members; an optimal, intermediate group size exists that maximizes the probability to produce the collective good.     

Hadza Cooperation

Strong reciprocity is an effective way to promote cooperation. This is especially true when one not only cooperates with cooperators and defects on defectors (second-party punishment) but even punishes those who defect on others (third-party, “altruistic” punishment). Some suggest we humans have a taste for such altruistic punishment and that this was important in the evolution of human cooperation. To assess this we need to look across a wide range of cultures. As part of a cross-cultural project, I played three experimental economics games with the Hadza, who are hunter-gatherers in Tanzania. The Hadza frequently engaged in second-party punishment but they rarely engaged in third-party punishment. Other small-scale societies engaged in less third-party punishment as well. I suggest third-party punishment only became more important in large, complex societies to solve more pressing collective-action problems.     

HUMAN COOPERATION BASED ON PUNISHMENT REPUTATION

The threat of punishment usually promotes cooperation. However, punishing itself is costly, rare in nonhuman animals, and humans who punish often finish with low payoffs in economic experiments. The evolution of punishment has therefore been unclear. Recent theoretical developments suggest that punishment has evolved in the context of reputation games. We tested this idea in a simple helping game with observers and with punishment and punishment reputation (experimentally controlling for other possible reputational effects). We show that punishers fully compensate their costs as they receive help more often. The more likely defection is punished within a group, the higher the level of within‐group cooperation. These beneficial effects perish if the punishment reputation is removed. We conclude that reputation is key to the evolution of punishment.     

The structure of mutations and the evolution of cooperation

Evolutionary game dynamics in finite populations assumes that all mutations are equally likely, i.e., if there are n strategies a single mutation can result in any strategy with probability 1/n. However, in biological systems it seems natural that not all mutations can arise from a given state. Certain mutations may be far away, or even be unreachable given the current composition of an evolving population. These distances between strategies (or genotypes) define a topology of mutations that so far has been neglected in evolutionary game theory. In this paper we re-evaluate classic results in the evolution of cooperation departing from the assumption of uniform mutations. We examine two cases: the evolution of reciprocal strategies in a repeated prisoner's dilemma, and the evolution of altruistic punishment in a public goods game. In both cases, alternative but reasonable mutation kernels shift known results in the direction of less cooperation. We therefore show that assuming uniform mutations has a substantial impact on the fate of an evolving population. Our results call for a reassessment of the "model-less" approach to mutations in evolutionary dynamics.