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

Group Cooperation without Group Selection: Modest Punishment Can Recruit Much Cooperation

Humans everywhere cooperate in groups to achieve benefits not attainable by individuals. Individual effort is often not automatically tied to a proportionate share of group benefits. This decoupling allows for free-riding, a strategy that (absent countermeasures) outcompetes cooperation. Empirically and formally, punishment potentially solves the evolutionary puzzle of group cooperation. Nevertheless, standard analyses appear to show that punishment alone is insufficient, because second-order free riders (those who cooperate but do not punish) can be shown to outcompete punishers. Consequently, many have concluded that other processes, such as cultural or genetic group selection, are required. Here, we present a series of agent-based simulations that show that group cooperation sustained by punishment easily evolves by individual selection when you introduce into standard models more biologically plausible assumptions about the social ecology and psychology of ancestral humans. We relax three unrealistic assumptions of past models. First, past models assume all punishers must punish every act of free riding in their group. We instead allow punishment to be probabilistic, meaning punishers can evolve to only punish some free riders some of the time. This drastically lowers the cost of punishment as group size increases. Second, most models unrealistically do not allow punishment to recruit labor; punishment merely reduces the punished agent’s fitness. We instead realistically allow punished free riders to cooperate in the future to avoid punishment. Third, past models usually restrict agents to interact in a single group their entire lives. We instead introduce realistic social ecologies in which agents participate in multiple, partially overlapping groups. Because of this, punitive tendencies are more expressed and therefore more exposed to natural selection. These three moves toward greater model realism reveal that punishment and cooperation easily evolve by direct selection—even in sizeable groups.

Neural components of altruistic punishment

Altruistic punishment, which occurs when an individual incurs a cost to punish in response to unfairness or a norm violation, may play a role in perpetuating cooperation. The neural correlates underlying costly punishment have only recently begun to be explored. Here we review the current state of research on the neural basis of altruism from the perspectives of costly punishment, emphasizing the importance of characterizing elementary neural processes underlying a decision to punish. In particular, we emphasize three cognitive processes that contribute to the decision to altruistically punish in most scenarios: inequity aversion, cost-benefit calculation, and social reference frame to distinguish self from others. Overall, we argue for the importance of understanding the neural correlates of altruistic punishment with respect to the core computations necessary to achieve a decision to punish.

Compassion meditators show less anger, less punishment, and more compensation of victims in response to fairness violations

Fairness violations elicit powerful behavioral and affective responses. Indeed, people are willing to incur costs to sanction unfair behavior. Here we study the possible impact of long-term mental training in socio-affective capacities such as compassion on altruistic punishment and compensatory behavior in economic games. To this end we recruited a group of long-term meditation practitioners (LTPs) who had engaged in an average of 40 K h of mental training exercises including compassion-related meditation, along with a group of meditation-naïve controls. Participants played several adaptations of the dictator game in which they had the opportunity to punish the dictator both when they were the recipients of the dictator's offer and when they were third-party witnesses to the dictator's treatment of an anonymous second player. Compared to controls, LTPs were less likely to punish when they were the victims of fairness violations. However, both groups punished equivalently when they witnessed others receiving unfair treatment. In post-task questionnaires, controls reported significantly more anger in response to unfair offers than LTPs, although fairness judgments did not differ between groups. These data suggest that because the LTPs were less angered by unfair treatment of themselves, they punished that behavior less. However, when they witnessed the unfair treatment of others, they engaged in norm-reinforcing punishment. Finally, when participants played an additional game which included the opportunity to recompense victims, LTPs were more likely to do so. Together these data point to differential approaches to justice whereby LTPs engaged less in vengeful, retributive justice and focused more on norm reinforcement and the restoration of equity. These differences suggest that social preferences are plastic and that altruistic responses to unfairness may be shaped by the prolonged cultivation of prosocial motivation, altruism, and compassion.

Direct and indirect punishment among strangers in the field

Many interactions in modern human societies are among strangers. Explaining cooperation in such interactions is challenging. The two most prominent explanations critically depend on individuals' willingness to punish defectors: In models of direct punishment, individuals punish antisocial behavior at a personal cost, whereas in models of indirect reciprocity, they punish indirectly by withholding rewards. We investigate these competing explanations in a field experiment with real-life interactions among strangers. We find clear evidence of both direct and indirect punishment. Direct punishment is not rewarded by strangers and, in line with models of indirect reciprocity, is crowded out by indirect punishment opportunities. The existence of direct and indirect punishment in daily life indicates the importance of both means for understanding the evolution of cooperation.

Both loved and feared: third party punishers are viewed as formidable and likeable, but these reputational benefits may only be open to dominant individuals

Third party punishment can be evolutionarily stable if there is heterogeneity in the cost of punishment or if punishers receive a reputational benefit from their actions. A dominant position might allow some individuals to punish at a lower cost than others and by doing so access these reputational benefits. Three vignette-based studies measured participants' judgements of a third party punisher in comparison to those exhibiting other aggressive/dominant behaviours (Study 1), when there was variation in the success of punishment (Study 2), and variation in the status of the punisher and the type of punishment used (Study 3). Third party punishers were judged to be more likeable than (but equally dominant as) those who engaged in other types of dominant behaviour (Study 1), were judged to be equally likeable and dominant whether their intervention succeeded or failed (Study 2), and participants believed that only a dominant punisher could intervene successfully (regardless of whether punishment was violent or non-violent) and that subordinate punishers would face a higher risk of retaliation (Study 3). The results suggest that dominance can dramatically reduce the cost of punishment, and that while individuals can gain a great deal of reputational benefit from engaging in third party punishment, these benefits are only open to dominant individuals. Taking the status of punishers into account may therefore help explain the evolution of third party punishment.

The value of vengeance and the demand for deterrence

Humans will incur costs to punish others who violate social norms. Theories of justice highlight 2 motives for punishment: a forward-looking deterrence of future norm violations and a backward-looking retributive desire to harm. Previous studies of costly punishment have not isolated how much people are willing to pay for retribution alone, because typically punishment both inflicts damage (satisfying the retributive motive) and communicates a norm violation (satisfying the deterrence motive). Here, we isolated retributive motives by examining how much people will invest in punishment when the punished individual will never learn about the punishment. Such “hidden” punishment cannot deter future norm violations but was nevertheless frequently used by both 2nd-party victims and 3rd-party observers of norm violations, indicating that retributive motives drive punishment decisions independently from deterrence goals. While self-reports of deterrence motives correlated with deterrence-related punishment behavior, self-reports of retributive motives did not correlate with retributive punishment behavior. Our findings reveal a preference for pure retribution that can lead to punishment without any social benefits.

Fair and unfair punishers coexist in the Ultimatum Game

In the Ultimatum Game, a proposer suggests how to split a sum of money with a responder. If the responder rejects the proposal, both players get nothing. Rejection of unfair offers is regarded as a form of punishment implemented by fair-minded individuals, who are willing to impose the cooperation norm at a personal cost. However, recent research using other experimental frameworks has observed non-negligible levels of antisocial punishment by competitive, spiteful individuals, which can eventually undermine cooperation. Using two large-scale experiments, this note explores the nature of Ultimatum Game punishers by analyzing their behavior in a Dictator Game. In both studies, the coexistence of two entirely different sub-populations is confirmed: prosocial punishers on the one hand, who behave fairly as dictators, and spiteful (antisocial) punishers on the other, who are totally unfair. The finding has important implications regarding the evolution of cooperation and the behavioral underpinnings of stable social systems.

Quality versus quantity of social ties in experimental cooperative networks

Recent studies suggest that allowing individuals to choose their partners can help to maintain cooperation in human social networks; this behaviour can supplement behavioural reciprocity, whereby humans are influenced to cooperate by peer pressure. However, it is unknown how the rate of forming and breaking social ties affects our capacity to cooperate. Here we use a series of online experiments involving 1,529 unique participants embedded in 90 experimental networks, to show that there is a ‘Goldilocks’ effect of network dynamism on cooperation. When the rate of change in social ties is too low, subjects choose to have many ties, even if they attach to defectors. When the rate is too high, cooperators cannot detach from defectors as much as defectors re-attach and, hence, subjects resort to behavioural reciprocity and switch their behaviour to defection. Optimal levels of cooperation are achieved at intermediate levels of change in social ties.

The effect of the rate of forming and breaking social ties on cooperative behaviour is not clear. Here the authors experimentally test the effect of rewiring the connections between individuals, and find that optimal levels of cooperation are achieved at intermediate levels of change in ties.

Punishment does not promote cooperation under exploration dynamics when anti-social punishment is possible

It has been argued that punishment promotes the evolution of cooperation when mutation rates are high (i.e. when agents engage in 'exploration dynamics'). Mutations maintain a steady supply of agents that punish free-riders, and thus free-riders are at a disadvantage. Recent experiments, however, have demonstrated that free-riders sometimes also pay to punish cooperators. Inspired by these empirical results, theoretical work has explored evolutionary dynamics where mutants are rare, and found that punishment does not promote the evolution of cooperation when this 'anti-social punishment' is allowed. Here we extend previous theory by studying the effect of anti-social punishment on the evolution of cooperation across higher mutation rates, and by studying voluntary as well as compulsory Public Goods Games. We find that for intermediate and high mutation rates, adding punishment does not promote cooperation in either compulsory or voluntary public goods games if anti-social punishment is possible. This is because mutations generate agents that punish cooperators just as frequently as agents that punish defectors, and these two effects cancel each other out. These results raise questions about the effectiveness of punishment for promoting cooperation when mutations are common, and highlight how decisions about which strategies to include in the strategy set can have profound effects on the resulting dynamics.

Justine effect: punishment of the unduly self-sacrificing cooperative individuals

BACKGROUND

Allowing players to punish their opponents in Public Goods Game sustains cooperation within a group and thus brings advantage to the cooperative individuals. However, the possibility of punishment of the co-players can result in antisocial punishment, the punishment of those players who contribute the most in the group. To better understand why antisocial punishment exists, it must be determined who are the anti-social punishers and who are their primary targets.

METHODS

For resolving these questions we increased the number of players in a group from usual four to twelve. Each group played six rounds of the standard Public Goods Game and six rounds of the Public Goods Game with punishment. Each player in each round received 20 CZK ($ 1.25). Players (N = 118) were rematched after each round so that they would not take into consideration opponents' past behavior.

RESULTS

The amount of the punishment received correlated negatively with the contribution (ρ = -0.665, p<0.001). However, this correlation was positive for players in the highest contributors-quartile (ρ = 0.254, p<0.001). Therefore, the graph of relation between the contribution given and punishment obtained was U-shaped (R2 = 0.678, p<0.001) with the inflection point near the left boarder of the upper quartile. The antisocial punishment was present in all groups, and in eight out of ten groups the Justine Effect (the positive correlation between the contribution to the public pool and the risk of suffering punishment in the subpopulation of altruistic players) emerged. In our sample, 22.5% subjects, all of them Free riders and low contributors, punished the altruistic players.

CONCLUSIONS

The results of our experimental game-study revealed the existence of the Justine effect--the positive correlation between the contribution to the public pool by a subpopulation of the most altruistic players, and the amount of punishment these players obtained from free-riders.

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.

The Evolution of Cooperation Through Institutional Incentives and Optional Participation

Rewards and penalties are common practical tools that can be used to promote cooperation in social institutions. The evolution of cooperation under reward and punishment incentives in joint enterprises has been formalized and investigated, mostly by using compulsory public good games. Recently, Sasaki et al. (2012, Proc Natl Acad Sci USA 109:1165-1169) considered optional participation as well as institutional incentives and described how the interplay between these mechanisms affects the evolution of cooperation in public good games. Here, we present a full classification of these cases of evolutionary dynamics. Specifically, whenever penalties are large enough to cause the bi-stability of both cooperation and defection in cases in which participation in the public good game is compulsory, these penalties will ultimately result in cooperation if participation in the public good game is optional. The global stability of coercion-based cooperation in this optional case contrasts strikingly with the bi-stability that is observed in the compulsory case. We also argue that optional participation is not as effective under rewards as under punishment.

If cooperation is likely punish mildly: insights from economic experiments based on the snowdrift game

Punishment may deter antisocial behavior. Yet to punish is costly, and the costs often do not offset the gains that are due to elevated levels of cooperation. However, the effectiveness of punishment depends not only on how costly it is, but also on the circumstances defining the social dilemma. Using the snowdrift game as the basis, we have conducted a series of economic experiments to determine whether severe punishment is more effective than mild punishment. We have observed that severe punishment is not necessarily more effective, even if the cost of punishment is identical in both cases. The benefits of severe punishment become evident only under extremely adverse conditions, when to cooperate is highly improbable in the absence of sanctions. If cooperation is likely, mild punishment is not less effective and leads to higher average payoffs, and is thus the much preferred alternative. Presented results suggest that the positive effects of punishment stem not only from imposed fines, but may also have a psychological background. Small fines can do wonders in motivating us to chose cooperation over defection, but without the paralyzing effect that may be brought about by large fines. The later should be utilized only when absolutely necessary.

Evolution of extortion in Iterated Prisoner's Dilemma games

Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the ability to use conditional strategies that depend on the outcome of previous interactions, thus allowing for reciprocation. Recently, a new class of strategies has been proposed, so-called "zero-determinant" strategies. These strategies enforce a fixed linear relationship between one's own payoff and that of the other player. A subset of those strategies allows "extortioners" to ensure that any increase in one player's own payoff exceeds that of the other player by a fixed percentage. Here, we analyze the evolutionary performance of this new class of strategies. We show that in reasonably large populations, they can act as catalysts for the evolution of cooperation, similar to tit-for-tat, but that they are not the stable outcome of natural selection. In very small populations, however, extortioners hold their ground. Extortion strategies do particularly well in coevolutionary arms races between two distinct populations. Significantly, they benefit the population that evolves at the slower rate, an example of the so-called "Red King" effect. This may affect the evolution of interactions between host species and their endosymbionts.

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.

Evolutionary dynamics of group interactions on structured populations: a review

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.

Reward from punishment does not emerge at all costs

The conundrum of cooperation has received increasing attention during the last decade. In this quest, the role of altruistic punishment has been identified as a mechanism promoting cooperation. Here we investigate the role of altruistic punishment on the emergence and maintenance of cooperation in structured populations exhibiting connectivity patterns recently identified as key elements of social networks. We do so in the framework of Evolutionary Game Theory, employing the Prisoner's Dilemma and the Stag-Hunt metaphors to model the conflict between individual and collective interests regarding cooperation. We find that the impact of altruistic punishment strongly depends on the ratio q/p between the cost of punishing a defecting partner (q) and the actual punishment incurred by the partner (p). We show that whenever q/p<1, altruistic punishment turns out to be detrimental for cooperation for a wide range of payoff parameters, when compared to the scenario without punishment. The results imply that while locally, the introduction of peer punishment may seem to reduce the chances of free-riding, realistic population structure may drive the population towards the opposite scenario. Hence, structured populations effectively reduce the expected beneficial contribution of punishment to the emergence of cooperation which, if not carefully dosed, may in fact hinder the chances of widespread cooperation.

Altruistic punishment — when a cooperative individual pays a cost to punish her defective partner — has been described as one of the mechanisms that help to explain cooperation's ubiquity in nature. Here, we investigate a model population where individuals interact with each other along the links of a network. The network is built so that it contains the relevant features of real social and biological interaction webs. Individuals engage in cooperation dilemmas with each other and have the possibility to punish defective partners in order to enforce higher cooperation levels. However, it turns out that the introduction of altruistic punishment not always promotes cooperation – in fact, it can actually hinder the spread of cooperation in a variety of cases that we are able to characterize. Effects acting at “micro”, individual level, such as softening the dilemma and reducing the pressure originating from the fear from being cheated and/or the temptation to cheat, can result in lower overall cooperation at a “macro”, population-wide level, due to the complex interference of the social dilemma and the heterogeneous interaction network.

The evolution of cooperation by social exclusion

The exclusion of freeriders from common privileges or public acceptance is widely found in the real world. Current models on the evolution of cooperation with incentives mostly assume peer sanctioning, whereby a punisher imposes penalties on freeriders at a cost to itself. It is well known that such costly punishment has two substantial difficulties. First, a rare punishing cooperator barely subverts the asocial society of freeriders, and second, natural selection often eliminates punishing cooperators in the presence of non-punishing cooperators (namely, 'second-order' freeriders). We present a game-theoretical model of social exclusion in which a punishing cooperator can exclude freeriders from benefit sharing. We show that such social exclusion can overcome the above-mentioned difficulties even if it is costly and stochastic. The results do not require a genetic relationship, repeated interaction, reputation or group selection. Instead, only a limited number of freeriders are required to prevent the second-order freeriders from eroding the social immune system.

Patient and impatient punishers of free-riders

Costly punishment of cheaters who contribute little or nothing to a cooperating group has been extensively studied, as an effective means to enforce cooperation. The prevailing view is that individuals use punishment to retaliate against transgressions of moral standards such as fairness or equity. However, there is much debate regarding the psychological underpinnings of costly punishment. Some authors suggest that costly punishment must be a product of humans' capacity for reasoning, self-control and long-term planning, whereas others argue that it is the result of an impulsive, present-oriented emotional drive. Here, we explore the inter-temporal preferences of punishers in a multilateral cooperation game and show that both interpretations might be right, as we can identify two different types of punishment: punishment of free-riders by cooperators, which is predicted by patience (future orientation); and free-riders' punishment of other free-riders, which is predicted by impatience (present orientation). Therefore, the picture is more complex as punishment by free-riders probably comes not from a reaction against a moral transgression, but instead from a competitive, spiteful drive. Thus, punishment grounded on morals may be related to lasting or delayed psychological incentives, whereas punishment triggered by competitive desires may be linked to short-run aspirations. These results indicate that the individual's time horizon is relevant for the type of social behaviour she opts for. Integrating such differences in inter-temporal preferences and the social behaviour of agents might help to achieve a better understanding of how human cooperation and punishment behaviour has evolved.

I dare you to punish me-vendettas in games of cooperation

Everybody has heard of neighbours, who have been fighting over some minor topic for years. The fight goes back and forth, giving the neighbours a hard time. These kind of reciprocal punishments are known as vendettas and they are a cross-cultural phenomenon. In evolutionary biology, punishment is seen as a mechanism for maintaining cooperative behaviour. However, this notion of punishment excludes vendettas. Vendettas pose a special kind of evolutionary problem: they incur high costs on individuals, i.e. costs of punishing and costs of being punished, without any benefits. Theoretically speaking, punishment should be rare in dyadic relationships and vendettas would not evolve under natural selection. In contrast, punishment is assumed to be more efficient in group environments which then can pave the way for vendettas. Accordingly, we found that under the experimental conditions of a prisoner's dilemma game, human participants punished only rarely and vendettas are scarce. In contrast, we found that participants retaliated frequently in the group environment of a public goods game. They even engaged in cost-intense vendettas (i.e. continuous retaliation), especially when the first punishment was unjustified or ambiguous. Here, punishment was mainly targeted at defectors in the beginning, but provocations led to mushrooming of counter-punishments. Despite the counter-punishing behaviour, participants were able to enhance cooperation levels in the public goods game. Few participants even seemed to anticipate the outbreak of costly vendettas and delayed their punishment to the last possible moment. Overall, our results highlight the importance of different social environments while studying punishment as a cooperation-enhancing mechanism.

Evolving righteousness in a corrupt world

Punishment offers a powerful mechanism for the maintenance of cooperation in human and animal societies, but the maintenance of costly punishment itself remains problematic. Game theory has shown that corruption, where punishers can defect without being punished themselves, may sustain cooperation. However, in many human societies and some insect ones, high levels of cooperation coexist with low levels of corruption, and such societies show greater wellbeing than societies with high corruption. Here we show that small payments from cooperators to punishers can destabilize corrupt societies and lead to the spread of punishment without corruption (righteousness). Righteousness can prevail even in the face of persistent power inequalities. The resultant righteous societies are highly stable and have higher wellbeing than corrupt ones. This result may help to explain the persistence of costly punishing behavior, and indicates that corruption is a sub-optimal tool for maintaining cooperation in human societies.

Punishment can promote defection in group-structured populations

Pro-social punishment, whereby cooperators punish defectors, is often suggested as a mechanism that maintains cooperation in large human groups. Importantly, models that support this idea have to date only allowed defectors to be the target of punishment. However, recent empirical work has demonstrated the existence of anti-social punishment in public goods games. That is, individuals that defect have been found to also punish cooperators. Some recent theoretical studies have found that such anti-social punishment can prevent the evolution of pro-social punishment and cooperation. However, the evolution of anti-social punishment in group-structured populations has not been formally addressed. Previous work has informally argued that group-structure must favour pro-social punishment. Here we formally investigate how two demographic factors, group size and dispersal frequency, affect selection pressures on pro- and anti-social punishment. Contrary to the suggestions of previous work, we find that anti-social punishment can prevent the evolution of pro-social punishment and cooperation under a range of group structures. Given that anti-social punishment has now been found in all studied extant human cultures, the claims of previous models showing the co-evolution of pro-social punishment and cooperation in group-structured populations should be re-evaluated.

Retaliation and antisocial punishment are overlooked in many theoretical models as well as behavioral experiments

Guala argues that there is a mismatch between most laboratory experiments on costly punishment and behavior in the field. In the lab, experimental designs typically suppress retaliation. The same is true for most theoretical models of the co-evolution of costly punishment and cooperation, which a priori exclude the possibility of defectors punishing cooperators.

Emergence of responsible sanctions without second order free riders, antisocial punishment or spite

While empirical evidence highlights the importance of punishment for cooperation in collective action, it remains disputed how responsible sanctions targeted predominantly at uncooperative subjects can evolve. Punishment is costly; in order to spread it typically requires local interactions, voluntary participation, or rewards. Moreover, theory and experiments indicate that some subjects abuse sanctioning opportunities by engaging in antisocial punishment (which harms cooperators), spiteful acts (harming everyone) or revenge (as a response to being punished). These arguments have led to the conclusion that punishment is maladaptive. Here, we use evolutionary game theory to show that this conclusion is premature: If interactions are non-anonymous, cooperation and punishment evolve even if initially rare, and sanctions are directed towards non-cooperators only. Thus, our willingness to punish free riders is ultimately a selfish decision rather than an altruistic act; punishment serves as a warning, showing that one is not willing to accept unfair treatments.

Leaving the loners alone: evolution of cooperation in the presence of antisocial punishment

The idea that voluntary participation may promote the evolution of cooperation and punishment in public good games has been recently called into question based on the study of the complete strategy set in which anyone can punish anyone else. If punishment actions are detached from contribution and participation in the game, the combination of punishment and voluntary participation no longer leads to high levels of cooperation. We show that this result crucially depends on specific details of the role of those who abstain from the collective endeavour, and only holds for a small subset of assumptions. If these loners are truly alone, cooperators who punish only defectors prevail, even when antisocial punishment is available.

Sustainable institutionalized punishment requires elimination of second-order free-riders

Although empirical and theoretical studies affirm that punishment can elevate collaborative efforts, its emergence and stability remain elusive. By peer-punishment the sanctioning is something an individual elects to do depending on the strategies in its neighborhood. The consequences of unsustainable efforts are therefore local. By pool-punishment, on the other hand, where resources for sanctioning are committed in advance and at large, the notion of sustainability has greater significance. In a population with free-riders, punishers must be strong in numbers to keep the "punishment pool" from emptying. Failure to do so renders the concept of institutionalized sanctioning futile. We show that pool-punishment in structured populations is sustainable, but only if second-order free-riders are sanctioned as well, and to a such degree that they cannot prevail. A discontinuous phase transition leads to an outbreak of sustainability when punishers subvert second-order free-riders in the competition against defectors.

Special agents can promote cooperation in the population

Cooperation is ubiquitous in our real life but everyone would like to maximize her own profits. How does cooperation occur in the group of self-interested agents without centralized control? Furthermore, in a hostile scenario, for example, cooperation is unlikely to emerge. Is there any mechanism to promote cooperation if populations are given and play rules are not allowed to change? In this paper, numerical experiments show that complete population interaction is unfriendly to cooperation in the finite but end-unknown Repeated Prisoner's Dilemma (RPD). Then a mechanism called soft control is proposed to promote cooperation. According to the basic idea of soft control, a number of special agents are introduced to intervene in the evolution of cooperation. They comply with play rules in the original group so that they are always treated as normal agents. For our purpose, these special agents have their own strategies and share knowledge. The capability of the mechanism is studied under different settings. We find that soft control can promote cooperation and is robust to noise. Meanwhile simulation results demonstrate the applicability of the mechanism in other scenarios. Besides, the analytical proof also illustrates the effectiveness of soft control and validates simulation results. As a way of intervention in collective behaviors, soft control provides a possible direction for the study of reciprocal behaviors.

Dynamic social networks promote cooperation in experiments with humans

Human populations are both highly cooperative and highly organized. Human interactions are not random but rather are structured in social networks. Importantly, ties in these networks often are dynamic, changing in response to the behavior of one's social partners. This dynamic structure permits an important form of conditional action that has been explored theoretically but has received little empirical attention: People can respond to the cooperation and defection of those around them by making or breaking network links. Here, we present experimental evidence of the power of using strategic link formation and dissolution, and the network modification it entails, to stabilize cooperation in sizable groups. Our experiments explore large-scale cooperation, where subjects' cooperative actions are equally beneficial to all those with whom they interact. Consistent with previous research, we find that cooperation decays over time when social networks are shuffled randomly every round or are fixed across all rounds. We also find that, when networks are dynamic but are updated only infrequently, cooperation again fails. However, when subjects can update their network connections frequently, we see a qualitatively different outcome: Cooperation is maintained at a high level through network rewiring. Subjects preferentially break links with defectors and form new links with cooperators, creating an incentive to cooperate and leading to substantial changes in network structure. Our experiments confirm the predictions of a set of evolutionary game theoretic models and demonstrate the important role that dynamic social networks can play in supporting large-scale human cooperation.

Evolution of altruistic punishment in heterogeneous populations

Evolutionary models for altruistic behavior typically make the assumption of homogeneity: each individual has the same costs and benefits associated with cooperating with each other and punishing for selfish behavior. In this paper, we relax this assumption by separating the population into heterogeneous classes, such that individuals from different classes differ in their ability to punish for selfishness. We compare the effects of introducing heterogeneity this way across two population models, that each represents a different type of population: the infinite and well-mixed population describes the way workers of social insects such as ants are organized, while a spatially structured population is more related to the way social norms evolve and are maintained in a social network. We find that heterogeneity in the effectiveness of punishment by itself has little to no effect on whether or not altruistic behavior will stabilize in a population. In contrast, heterogeneity in the cost that individuals pay to punish for selfish behavior allows altruistic behavior to be maintained more easily. Fewer punishers are needed to deter selfish behavior, and the individuals that punish will mostly belong to the class that pays a lower cost to do so. This effect is amplified when individuals that pay a lower cost for punishing inflict a higher punishment. The two population models differ when individuals that pay a low cost for punishing also inflict a lower punishment. In this situation, altruistic behavior becomes harder to maintain in an infinite and well-mixed population. However, this effect does not occur when the population is spatially structured.

The evolution of antisocial punishment in optional public goods games

Cooperation, where one individual incurs a cost to help another, is a fundamental building block of the natural world and human society. It has been suggested that costly punishment can promote the evolution of cooperation, with the threat of punishment deterring free-riders. Recent experiments, however, have revealed the existence of 'antisocial' punishment, where non-cooperators punish cooperators. While various theoretical models find that punishment can promote the evolution of cooperation, these models a priori exclude the possibility of antisocial punishment. Here we extend the standard theory of optional public goods games to include the full set of punishment strategies. We find that punishment no longer increases cooperation, and that selection favours substantial levels of antisocial punishment for a wide range of parameters. Furthermore, we conduct behavioural experiments, showing results consistent with our model predictions. As opposed to an altruistic act that promotes cooperation, punishment is mostly a self-interested tool for protecting oneself against potential competitors.

Green-beard effect predicts the evolution of traitorousness in the two-tag Prisoner's dilemma

Cooperation, a costly interaction in which individuals benefit one another, plays a crucial role in many of the major transitions of evolution. Yet, as illustrated by the Prisoner's dilemma, cooperative systems are fragile because cooperators can be exploited by defectors who reap the benefits of cooperation but do not reciprocate. This barrier to cooperation may be overcome if cooperators have a recognisable phenotypic tag that allows them to adopt the conditional strategy of cooperating with fellow tag-mates while defecting against others, a mechanism known as the 'green-beard effect'. The resulting intra-tag cooperator strategy is particularly effective in structured populations where local clumps of cooperative tag-mates can find refuge. While intra-tag cooperation is robust against unconditional defectors in the spatial Prisoner's dilemma (at least when the cost of cooperation is low), the role of extra-tag cooperators - individuals who cooperate only with those bearing a different tag - has received little attention, despite the fact that these traitors form mixed-tag aggregations whose heterogeneous makeup potentially allows the exploitation of multiple other strategies. Using a spatial model of the two-tag Prisoner's dilemma, I show that extra-tag cooperation readily evolves under low to intermediate cost-benefit ratios of mutual cooperation (r). Specifically, at low r, mixed-tag aggregations of extra-tag cooperators take over the population, while at intermediate r, such aggregations coexist with intra-tag cooperators and unconditional defectors with whom they engage in non-transitive spatial invasibility. In systems with more than two tags, however, the dilution of extra-tag cooperators within mixed-tag aggregations prevents the strategy from being effective. Thus, the same beard chromodynamics that promotes within-group cooperation also predicts the evolution of traitorous between-group cooperation, but only when the number of beard colours is low.

Male cleaner wrasses adjust punishment of female partners according to the stakes

Punishment is an important deterrent against cheating in cooperative interactions. In humans, the severity of cheating affects the strength of punishment which, in turn, affects the punished individual's future behaviour. Here, we show such flexible adjustments for the first time in a non-human species, the cleaner wrasse (Labroides dimidiatus), where males are known to punish female partners. We exposed pairs of cleaners to a model client offering two types of food, preferred 'prawn' items and less-preferred 'flake' items. Analogous to interactions with real clients, eating a preferred prawn item ('cheating') led to model client removal. We varied the extent to which female cheating caused pay-off reduction to the male and measured the corresponding severity of male punishment. Males punished females more severely when females cheated during interactions with high value, rather than low value, model clients; and when females were similar in size to the male. This pattern may arise because, in this protogynous hermaphrodite, cheating by similar-sized females may reduce size differences to the extent that females change sex and become reproductive competitors. In response to more severe punishment from males, females behaved more cooperatively. Our results show that punishment can be adjusted to circumstances and that such subtleties can have an important bearing on the outcome of cooperative interactions.

Costly punishment prevails in intergroup conflict

Understanding how societies resolve conflicts between individual and common interests remains one of the most fundamental issues across disciplines. The observation that humans readily incur costs to sanction uncooperative individuals without tangible individual benefits has attracted considerable attention as a proximate cause as to why cooperative behaviours might evolve. However, the proliferation of individually costly punishment has been difficult to explain. Several studies over the last decade employing experimental designs with isolated groups have found clear evidence that the costs of punishment often nullify the benefits of increased cooperation, rendering the strong human tendency to punish a thorny evolutionary puzzle. Here, we show that group competition enhances the effectiveness of punishment so that when groups are in direct competition, individuals belonging to a group with punishment opportunity prevail over individuals in a group without this opportunity. In addition to competitive superiority in between-group competition, punishment reduces within-group variation in success, creating circumstances that are highly favourable for the evolution of accompanying group-functional behaviours. We find that the individual willingness to engage in costly punishment increases with tightening competitive pressure between groups. Our results suggest the importance of intergroup conflict behind the emergence of costly punishment and human cooperation.

Local replicator dynamics: a simple link between deterministic and stochastic models of evolutionary game theory

Classical replicator dynamics assumes that individuals play their games and adopt new strategies on a global level: Each player interacts with a representative sample of the population and if a strategy yields a payoff above the average, then it is expected to spread. In this article, we connect evolutionary models for infinite and finite populations: While the population itself is infinite, interactions and reproduction occurs in random groups of size N. Surprisingly, the resulting dynamics simplifies to the traditional replicator system with a slightly modified payoff matrix. The qualitative results, however, mirror the findings for finite populations, in which strategies are selected according to a probabilistic Moran process. In particular, we derive a one-third law that holds for any population size. In this way, we show that the deterministic replicator equation in an infinite population can be used to study the Moran process in a finite population and vice versa. We apply the results to three examples to shed light on the evolution of cooperation in the iterated prisoner's dilemma, on risk aversion in coordination games and on the maintenance of dominated strategies.

Infectious disease modeling of social contagion in networks

Many behavioral phenomena have been found to spread interpersonally through social networks, in a manner similar to infectious diseases. An important difference between social contagion and traditional infectious diseases, however, is that behavioral phenomena can be acquired by non-social mechanisms as well as through social transmission. We introduce a novel theoretical framework for studying these phenomena (the SISa model) by adapting a classic disease model to include the possibility for ‘automatic’ (or ‘spontaneous’) non-social infection. We provide an example of the use of this framework by examining the spread of obesity in the Framingham Heart Study Network. The interaction assumptions of the model are validated using longitudinal network transmission data. We find that the current rate of becoming obese is 2 per year and increases by 0.5 percentage points for each obese social contact. The rate of recovering from obesity is 4 per year, and does not depend on the number of non-obese contacts. The model predicts a long-term obesity prevalence of approximately 42, and can be used to evaluate the effect of different interventions on steady-state obesity. Model predictions quantitatively reproduce the actual historical time course for the prevalence of obesity. We find that since the 1970s, the rate of recovery from obesity has remained relatively constant, while the rates of both spontaneous infection and transmission have steadily increased over time. This suggests that the obesity epidemic may be driven by increasing rates of becoming obese, both spontaneously and transmissively, rather than by decreasing rates of losing weight. A key feature of the SISa model is its ability to characterize the relative importance of social transmission by quantitatively comparing rates of spontaneous versus contagious infection. It provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviors, health states, ideas or diseases with reservoirs.

Information, trends, behaviors and even health states may spread between contacts in a social network, similar to disease transmission. However, a major difference is that as well as being spread infectiously, it is possible to acquire this state spontaneously. For example, you can gain knowledge of a particular piece of information either by being told about it, or by discovering it yourself. In this paper we introduce a mathematical modeling framework that allows us to compare the dynamics of these social contagions to traditional infectious diseases. We can also extract and compare the rates of spontaneous versus contagious acquisition of a behavior from longitudinal data and can use this to predict the implications for future prevalence and control strategies. As an example, we study the spread of obesity, and find that the current rate of becoming obese is about 2 per year and increases by 0.5 percentage points for each obese social contact, while the rate of recovering from obesity is 4 per year. The rates of spontaneous infection and transmission have steadily increased over time since 1970, driving the increase in obesity prevalence. Our model thus provides a quantitative way to analyze the strength and implications of social contagions.