Public goods games with reward in finite populations

Public goods games paraphrase the problem of cooperation in game theoretical terms. Cooperators contribute to a public good and thereby increase the welfare of others at a cost to themselves. Defectors consume the public good but do not pay its cost and therefore outperform cooperators. Hence, according to genetic or cultural evolution, defectors should be favored and the public good disappear – despite the fact that groups of cooperators are better off than groups of defectors. The maximization of short term individual profits causes the demise of the common resource to the detriment of all. This outcome can be averted by introducing incentives to cooperate. Negative incentives based on the punishment of defectors efficiently stabilize cooperation once established but cannot initiate cooperation. Here we consider the complementary case of positive incentives created by allowing individuals to reward those that contribute to the public good. The finite-population stochastic dynamics of the public goods game with reward demonstrate that reward initiates cooperation by providing an escape hatch out of states of mutual defection. However, in contrast to punishment, reward is unable to stabilize cooperation but, instead, gives rise to a persistent minority of cooperators.     

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.     

Persistent cooperators in nature

The evolution and maintenance of cooperation fascinated researchers for several decades. Recently, theoretical models and experimental evidence show that costly punishment may facilitate cooperation in human societies. The puzzle how the costly punishment behaviour evolves can be solved under voluntary participation. Could the punishers emerge if participation is compulsory? Is the punishment inevitably a selfish behaviour or an altruistic behaviour? The motivations behind punishment are still an enigma. Based on public goods interactions, we present a model in which just a certain portion of the public good is divided equally among all members. The other portion is distributed to contributors when paying a second cost. The contributors who are willing to pay a second cost are called the persistent cooperators (PC), indicating their desire to retrieve the proportion of the payoff derived from their own contributions with persistent efforts. We show that the persistent cooperators can be costly punishers, which may account for the origin of human costly punishment behaviour under compulsory participation. In this sense our models may show theoretically that the original motivation behind punishment is to retrieve deserved payoff from their own contributions, a selfish incentive. But the persistent cooperators can also flourish or dominate the population in other situations. We list many real examples in which contributors are the persistent cooperators, and they benefit. This indicates a simple norm promoting cooperation: contributing more and gaining more.     

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.     

Interactions between personality and institutions in cooperative behaviour in humans

Laboratory attempts to identify relationships between personality and cooperative behaviour in humans have generated inconsistent results. This may partially stem from different practices in psychology and economics laboratories, with both hypothetical players and incentives typical only in the former. Another possible cause is insufficient consideration of the contexts within which social dilemmas occur. Real social dilemmas are often governed by institutions that change the payoff structure via rewards and punishments. However, such ‘strong situations’ will not necessarily suppress the effects of personality. On the contrary, they may affect some personalities differentially. Extraversion and neuroticism, reflecting variation in reward and punishment sensitivity, should predict modification of cooperative behaviour following changes to the payoff structure. We investigate interactions between personality and a punishment situation via two versions of a public goods game. We find that, even in a strong situation, personality matters and, moreover, it is related to strategic shifts in cooperation. Extraversion is associated with a shift from free-riding to cooperation in the presence of punishment, agreeableness is associated with initially higher contributions regardless of game, and, contrary to our predictions, neuroticism is associated with lower contributions regardless of game. Results should lead to new hypotheses that relate variation in biological functioning to individual differences in cooperative behaviour and that consider three-way interactions among personality, institutional context and sociocultural background.     

An Evolutionary Model of Cooperation,Fairness and Altruistic Punishment in Public Good Games

We identify and explain the mechanisms that account for the emergence of fairness preferences and altruistic punishment in voluntary contribution mechanisms by combining an evolutionary perspective together with an expected utility model. We aim at filling a gap between the literature on the theory of evolution applied to cooperation and punishment, and the empirical findings from experimental economics. The approach is motivated by previous findings on other-regarding behavior, the co-evolution of culture, genes and social norms, as well as bounded rationality. Our first result reveals the emergence of two distinct evolutionary regimes that force agents to converge either to a defection state or to a state of coordination, depending on the predominant set of self- or other-regarding preferences. Our second result indicates that subjects in laboratory experiments of public goods games with punishment coordinate and punish defectors as a result of an aversion against disadvantageous inequitable outcomes. Our third finding identifies disadvantageous inequity aversion as evolutionary dominant and stable in a heterogeneous population of agents endowed initially only with purely self-regarding preferences. We validate our model using previously obtained results from three independently conducted experiments of public goods games with punishment.     

The Effect of Ostracism and Optional Participation on the Evolution of Cooperation in the Voluntary Public Goods Game

Not only animals, plants and microbes but also humans cooperate in groups. The evolution of cooperation in a group is an evolutionary puzzle, because defectors always obtain a higher benefit than cooperators. When people participate in a group, they evaluate group member’s reputations and then decide whether to participate in it. In some groups, membership is open to all who are willing to participate in the group. In other groups, a candidate is excluded from membership if group members regard the candidate’s reputation as bad. We developed an evolutionary game model and investigated how participation in groups and ostracism influence the evolution of cooperation in groups when group members play the voluntary public goods game, by means of computer simulation. When group membership is open to all candidates and those candidates can decide whether to participate in a group, cooperation cannot be sustainable. However, cooperation is sustainable when a candidate cannot be a member unless all group members admit them to membership. Therefore, it is not participation in a group but rather ostracism, which functions as costless punishment on defectors, that is essential to sustain cooperation in the voluntary public goods game.     

Self-serving punishment of a common enemy creates a public good in reef fishes

A key challenge for evolutionary biologists is to determine conditions under which individuals benefit from a contribution to public goods [1, 2]. For humans, it has been observed that punishment of free riders may promote contributions [3,?4], but the conditions that lead to stable cooperation based on punishment remain hotly debated [5-8]. Here we present empirical evidence that public goods may emerge as a by-product of self-serving punishment in interactions between coral reef fishes and parasitic saber-tooth blennies that stealthily attack their fish victims from behind to take a bite [9]. We first show that chasing the blenny functions as punishment [10], because it decreases the probability of future attacks. We then provide evidence that in female scalefin anthias, a shoaling species, punishment creates a public good because it increases the probability that the parasite switches to another species for the next attack. A final experiment suggests that punishment is nevertheless self-serving because blennies appear to be able to discriminate between look-alike punishers and nonpunishers. Thus, individuals that do contribute to the public good may risk being identified by the parasite as easy targets for future attacks.     

Exit,Punishment and Rewards in Commons Dilemmas: An Experimental Study

Commons dilemmas are interaction situations where a common good is provided or exploited by a group of individuals so that optimal collective outcomes clash with private interests. Although in these situations, social norms and institutions exist that might help individuals to cooperate, little is known about the interaction effects between positive and negative incentives and exit options by individuals. We performed a modified public good game experiment to examine the effect of exit, rewards and punishment, as well as the interplay between exit and rewards and punishment. We found that punishment had a stronger effect than rewards on cooperation if considered by itself, whereas rewards had a stronger effect when combined with voluntary participation. This can be explained in terms of the ‘framing effect’, i.e., as the combination of exit and rewards might induce people to attach higher expected payoffs to cooperative strategies and expect better behaviour from others.     

Replicator dynamics of reward & reputation in public goods games

Public goods games have become the mathematical metaphor for game theoretical investigations of cooperative behavior in groups of interacting individuals. Cooperation is a conundrum because cooperators make a sacrifice to benefit others at some cost to themselves. Exploiters or defectors reap the benefits and forgo costs. Despite the fact that groups of cooperators outperform groups of defectors, Darwinian selection or utilitarian principles based on rational choice should favor defectors. In order to overcome this social dilemma, much effort has been expended for investigations pertaining to punishment and sanctioning measures against defectors. Interestingly, the complementary approach to create positive incentives and to reward cooperation has received considerably less attention—despite being heavily advocated in education and social sciences for increasing productivity or preventing conflicts. Here we show that rewards can indeed stimulate cooperation in interaction groups of arbitrary size but, in contrast to punishment, fail to stabilize it. In both cases, however, reputation is essential. The combination of reward and reputation result in complex dynamics dominated by unpredictable oscillations.     

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.     

人类的利他性惩罚：认知神经科学的视角

利他性惩罚广泛存在于人类社会中,在群体合作与规范维护方面起着重要的积极作用．个体作为潜在的惩罚者,从知觉到不公平事件到做出惩罚行为,需要经过一系列的认知和情绪过程,包括公平判断、奖赏加工、自我控制以及心理化等过程,并且调用相应的神经生理机制．认知神经科学为理解人类的利他性惩罚行为提供了新的视角和方法．本文基于最新的研究发现,综述了利他性惩罚相关的神经生理基础．     

Strict or Graduated Punishment? Effect of Punishment Strictness on the Evolution of Cooperation in Continuous Public Goods Games

Whether costly punishment encourages cooperation is one of the principal questions in studies on the evolution of cooperation and social sciences. In society, punishment helps deter people from flouting rules in institutions. Specifically, graduated punishment is a design principle for long-enduring common-pool resource institutions. In this study, we investigate whether graduated punishment can promote a higher cooperation level when each individual plays the public goods game and has the opportunity to punish others whose cooperation levels fall below the punisher’s threshold. We then examine how spatial structure affects evolutionary dynamics when each individual dies inversely proportional to the game score resulting from the social interaction and another player is randomly chosen from the population to produce offspring to fill the empty site created after a player’s death. Our evolutionary simulation outcomes demonstrate that stricter punishment promotes increased cooperation more than graduated punishment in a spatially structured population, whereas graduated punishment increases cooperation more than strict punishment when players interact with randomly chosen opponents from the population. The mathematical analysis also supports the results.     

Human altruism: economic, neural, and evolutionary perspectives

Human cooperation represents a spectacular outlier in the animal world. Unlike other creatures, humans frequently cooperate with genetically unrelated strangers, often in large groups, with people they will never meet again, and when reputation gains are small or absent. Experimental evidence and evolutionary models suggest that strong reciprocity, the behavioral propensity for altruistic punishment and altruistic rewarding, is of key importance for human cooperation. Here, we review both evidence documenting altruistic punishment and altruistic cooperation and recent brain imaging studies that combine the powerful tools of behavioral game theory with neuroimaging techniques. These studies show that mutual cooperation and the punishment of defectors activate reward related neural circuits, suggesting that evolution has endowed humans with proximate mechanisms that render altruistic behavior psychologically rewarding.     

Power and corruption

Cooperation is ubiquitous in the natural world. What seems nonsensical is why natural selection favors a behavior whereby individuals would lose out by benefiting their competitor. This conundrum, for almost half a century, has puzzled scientists and remains a fundamental problem in biology, psychology, and economics. In recent years, the explanation that punishment can maintain cooperation has received much attention. Individuals who punish noncooperators thrive when punishment does not entail a cost to the punisher. However when punishment is costly, cooperation cannot be preserved. Most literature on punishment fails to consider that punishers may act corruptly by not cooperating when punishing noncooperators. No research has considered that there might be power asymmetries between punishers and nonpunishers that turn one of these type of individuals more or less susceptible to experiencing punishment. Here, we formulate a general game allowing corruption and power asymmetries between punishers and nonpunishers. We show that cooperation can persist if punishers possess power and use it to act corruptly. This result provides a new interpretation of recent data on corrupt policing in social insects and the psychology of power and hypocrisy in humans. These results suggest that corruption may play an important role in maintaining cooperation in insects and human societies. In contrast with previous research, we contend that costly punishment can be beneficial for social groups. This work allows us to identify ways in which corruption can be used to the advantage of a society.     

The Computational Development of Reinforcement Learning during Adolescence

Adolescence is a period of life characterised by changes in learning and decision-making. Learning and decision-making do not rely on a unitary system, but instead require the coordination of different cognitive processes that can be mathematically formalised as dissociable computational modules. Here, we aimed to trace the developmental time-course of the computational modules responsible for learning from reward or punishment, and learning from counterfactual feedback. Adolescents and adults carried out a novel reinforcement learning paradigm in which participants learned the association between cues and probabilistic outcomes, where the outcomes differed in valence (reward versus punishment) and feedback was either partial or complete (either the outcome of the chosen option only, or the outcomes of both the chosen and unchosen option, were displayed). Computational strategies changed during development: whereas adolescents’ behaviour was better explained by a basic reinforcement learning algorithm, adults’ behaviour integrated increasingly complex computational features, namely a counterfactual learning module (enabling enhanced performance in the presence of complete feedback) and a value contextualisation module (enabling symmetrical reward and punishment learning). Unlike adults, adolescent performance did not benefit from counterfactual (complete) feedback. In addition, while adults learned symmetrically from both reward and punishment, adolescents learned from reward but were less likely to learn from punishment. This tendency to rely on rewards and not to consider alternative consequences of actions might contribute to our understanding of decision-making in adolescence.     

Cooperation as a volunteer’s dilemma and the strategy of conflict in public goods games

Conflict and cooperation for the exploitation of public goods are usually modelled as an N‐person prisoner’s dilemma. Many social dilemmas, however, would be described more properly as a volunteer’s dilemma, in which a certain number of individuals are necessary to produce a public good. If volunteering is costly, but so is failure to produce the public good, cheaters can invade and form a stable mixed equilibrium with cooperators. The dilemma is that the benefit for the group decreases with group size because the larger the group is, the less likely it is that someone volunteers. This problem persists even in the presence of a high degree of relatedness between group members. This model provides precise, testable predictions for the stability of cooperation. It also suggests a counterintuitive but practical solution for this kind of social dilemmas: increasing the damage resulting from the failure to produce the public good increases the probability that the public good is actually produced. Adopting a strategy that entails a deliberate risk (brinkmanship), therefore, can lead to a benefit for the society without being detrimental for the individual.     

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 cost of cowardice: punitive sentiments towards free riders in Turkana raids

Models indicate that large-scale cooperation can be sustained by indirect reciprocity or direct punishment, but the relative importance of these mechanisms is unresolved. Unlike direct punishment, indirect sanctions can be meted out without cost to the sanctioner, but direct punishment is advantageous when the scale of cooperation exceeds the network size of individuals. It is of great interest to assess the importance of these mechanisms in small-scale acephalous groups in which people have lived for most of our evolutionary history. Here we evaluate sentiments towards free riders in combat among the Turkana, an acephalous nomadic pastoral society in East Africa who periodically mobilize for cattle-raids against neighboring ethnic groups. Using vignette studies, we probed participants’ motivation to sanction fictitious warriors who were cowards or deserters in a raid and compared it respectively to their reactions to an unskilled warrior or a warrior who turns back due to illness. Our results indicate that the Turkana are motivated to impose both indirect and direct sanctions on cowards consistent with indirect reciprocity and punishment models of cooperation. Our findings imply that both these mechanisms have shaped human cooperative psychology, and sheds light on how prestate societies solve the collective action problem in warfare.     

No Evidence for Moral Reward and Punishment in an Anonymous Context

Human social interactions are regulated by moral norms that define individual obligations and rights. These norms are enforced by punishment of transgressors and reward of followers. Yet, the generality and strength of this drive to punish or reward is unclear, especially when people are not personally involved in the situation and when the actual impact of their sanction is only indirect, i.e., when it diminishes or promotes the social status of the punished or rewarded individual. In a real-life study, we investigated if people are inclined to anonymously punish or reward a person for her past deeds in a different social context. Participants from three socio-professional categories voted anonymously for early career violinists in an important violin competition. We found that participants did not punish an immoral violin candidate, nor did they reward another hyper-moral candidate. On the contrary, one socio-professional category sanctioned hyper-morality. Hence, salient moral information about past behavior did not elicit punishment or reward in an impersonal situation where the impact of the sanction was indirect. We conclude that contextual features play an important role in human motivation to enforce moral norms.