THE EVOLUTION OF PUNISHMENT IN n-PLAYER PUBLIC GOODS GAMES: A VOLUNTEER'S DILEMMA

Risk, sanctions and norm change: the formation and decay of social distancing norms

Global challenges like the climate crisis and pandemic outbreaks require collective responses where people quickly adapt to changing circumstances. Social norms are potential solutions, but only if they themselves are flexible enough. The COVID-19 pandemic provided a unique opportunity to study norm formation and decay in real-world contexts. We tracked empirical and normative expectations about social distancing and empirical and normative expectations of sanctioning from June 2021 to February 2022 to explore how norms and meta norms evolved as COVID-19 risk decreased and increased. We found that norms and meta norms partially coevolve with risk dynamics, although they recover with some delay. This implies that norms should be enforced as soon as risk increases. We therefore tested how sanctioning intentions vary for different hypothetical norms and find them to increase with a clear meta norm of sanctioning, yet decrease with a clear social norm of distance. In conclusion, social norms evolve spontaneously with changing risk, but might not be adaptive enough when the lack of meta norms of sanctioning introduce tolerance for norm violations. Moreover, norm nudges can potentially have negative externalities if strengthening the social norm increases tolerance for norm violations. These results put some limits to social norms as solutions to guide behaviour under risk. This article is part of the theme issue 'Social norm change: drivers and consequences'.

The shirker's dilemma and the prospect of cooperation in large groups

Cooperation usually becomes harder to sustain as groups become larger because incentives to shirk increase with the number of potential contributors to collective action. But is this always the case? Here we study a binary-action cooperative dilemma where a public good is provided as long as not more than a given number of players shirk from a costly cooperative task. We find that at the stable polymorphic equilibrium, which exists when the cost of cooperation is low enough, the probability of cooperating increases with group size and reaches a limit of one when the group size tends to infinity. Nevertheless, increasing the group size may increase or decrease the probability that the public good is provided at such an equilibrium, depending on the cost value. We also prove that the expected payoff to individuals at the stable polymorphic equilibrium (i.e., their fitness) decreases with group size. For low enough costs of cooperation, both the probability of provision of the public good and the expected payoff converge to positive values in the limit of large group sizes. However, we also find that the basin of attraction of the stable polymorphic equilibrium is a decreasing function of group size and shrinks to zero in the limit of very large groups. Overall, we demonstrate non-trivial comparative statics with respect to group size in an otherwise simple collective action problem.

Direct punishment and indirect reputation-based tactics to intervene against offences

Punishment and reputation-based mechanisms play a major role in supporting the evolution of human cooperation. Theoretical accounts and field observations suggest that humans use multiple tactics to intervene against offences-including confrontation, gossip and ostracism-which have unique benefits and costs. Here, we draw a distinction between direct punishment tactics (i.e. physical and verbal confrontation) and indirect reputation-based tactics (i.e. gossip and ostracism). Based on this distinction, we sketch the common and unique social functions that different tactics are tailored to serve and describe information-processing mechanisms that potentially underlie decisions concerning how to intervene against offences. We propose that decision rules guiding direct and indirect tactics should weigh information about the benefits of changing others' behaviour versus the costs of potential retaliation. Based on a synthesis of existing evidence, we highlight the role of situational, relational and emotional factors in motivating distinct punishment tactics. We suggest that delineating between direct and indirect tactics can inform debates about the prevalence and functions of punishment and the reputational consequences of third-party intervention against offences. We emphasize the need to study how people use reputation-based tactics for partner recalibration and partner choice, within interdependent relationships and social networks, and in daily life situations. This article is part of the theme issue 'The language of cooperation: reputation and honest signalling'.

Punishment: one tool, many uses

Humans are outstanding in their ability to cooperate with unrelated individuals, and punishment - paying a cost to harm others - is thought to be a key supporting mechanism. According to this view, cooperators punish defectors, who respond by behaving more cooperatively in future interactions. However, a synthesis of the evidence from laboratory and real-world settings casts serious doubts on the assumption that the sole function of punishment is to convert cheating individuals into cooperators. Instead, punishment often prompts retaliation and punishment decisions frequently stem from competitive, rather than deterrent motives. Punishment decisions often reflect the desire to equalise or elevate payoffs relative to targets, rather than the desire to enact revenge for harm received or to deter cheats from reoffending in future. We therefore suggest that punishment also serves a competitive function, where what looks like spiteful behaviour actually allows punishers to equalise or elevate their own payoffs and/or status relative to targets independently of any change in the target's behaviour. Institutions that reduce or remove the possibility that punishers are motivated by relative payoff or status concerns might offer a way to harness these competitive motives and render punishment more effective at restoring cooperation.

Evolution of coordinated punishment to enforce cooperation from an unbiased strategy space

The emergence and maintenance of punishment to protect the commons remains an open puzzle in social and biological sciences. Even in societies where pro-social punishing is common, some individuals seek to cheat the system if they see a chance to do so—and public goods are often maintained in spite of cheaters who do not contribute. We present a model accounting for all possible strategies in a public goods game with punishment. While most models of punishment restrict the set of possible behaviours, excluding seemingly paradoxical anti-social strategies from the start, we show that these strategies can play an important role in explaining large-scale cooperation as observed in human societies. We find that coordinated punishment can emerge from individual interactions, but the stability of the associated institutions is limited owing to anti-social and opportunistic behaviour. In particular, coordinated anti-social punishment can undermine cooperation if individuals cannot condition their behaviour on the existence of institutions that punish. Only when we allow for observability and conditional behaviours do anti-social strategies no longer threaten cooperation. This is due to a stable coexistence of a minority supporting pro-social institutions and those who only cooperate if such institutions are in place. This minority of supporters is enough to guarantee substantial cooperation under a wide range of conditions. Our findings resonate with the empirical observation that public goods are resilient to opportunistic cheaters in large groups of unrelated individuals. They also highlight the importance of letting evolution, and not modellers, decide which strategies matter.

Heterogeneous groups overcome the diffusion of responsibility problem in social norm enforcement

Social norms promote cooperation in everyday life because many people are willing to negatively sanction norm breakers at a cost to themselves. However, a norm violation may persist if only one person is required to sanction the norm breaker and everyone expects someone else to do it. Here we employ the volunteer's dilemma game (VOD) to model this diffusion of responsibility in social norm enforcement. The symmetric VOD is a binary choice game in which all actors have the same costs of and benefits from cooperation and only one actor's cooperation is required to provide the collective good for the group. The asymmetric VOD differs from the symmetric VOD in one (strong) actor having lower costs of cooperation. In a laboratory experiment, we find that, in line with the diffusion of responsibility hypothesis, subjects' propensities to sanction the norm breaker decrease with group size in the symmetric VOD. In the asymmetric VOD, groups tacitly coordinate on the strong subject to sanction the norm breaker alone. Although at first lower in larger groups, strong subjects' sanctioning rates increase over time and reach equally high levels across different group sizes. Our results show that heterogeneous groups can be more effective in achieving norm compliance than groups of all equals because they naturally evade diffusion of responsibility in social norm enforcement.

Cheater-altruist synergy in public goods games

Much research has focused on the deleterious effects of free-riding in public goods games, and a variety of mechanisms that suppress cheating behavior. Here we argue that under certain conditions cheating can be beneficial to the population. In a public goods game, cheaters do not pay for the cost of the public goods, yet they receive the benefit. Although this free-riding harms the entire population in the long run, the success of cheaters may aid the population when there is a common enemy that antagonizes both cooperators and cheaters. Here we study models of the interactions between tumor cells, which play a public goods game, and the immune system. We investigate three population dynamics models of cancer growth combined with a model of effector cell dynamics. We show that under a public good with a limiting benefit, the presence of cheaters aids the tumor in overcoming immune system suppression, and explore the parameter space wherein it occurs. The mechanism of this phenomenon is that a polymorphism of cheaters and altruists optimizes the average growth rate of the tumor, which is what determines whether or not the immune response is overcome. Our results give support for a possible synergy between cooperators and cheaters in ecological public goods games.

Love or fear: can punishment promote cooperation?

Cooperation is a paradox: Why should one perform a costly behavior only to increase the fitness of another? Human societies, in which individuals cooperate with genetically unrelated individuals on a considerably larger scale than most mammals do, are especially puzzling in this regard. Recently, the threat of punishment has been given substantial attention as one of the mechanisms that could help sustain human cooperation in such situations. Nevertheless, using punishment to explain cooperation only leads to further questions: Why spend precious resources to penalize free-riders, especially if others can avoid this investment and cheaters can punish you back? Here, it is argued that current evidence supports punishment as an efficient means for the maintenance of cooperation, and that the gravity of proposed limitations of punishment for maintaining cooperation may have been overestimated in previous studies due to the features of experimental design. Most notably, the importance of factors as characteristic of human societies as reputation and language has been greatly neglected. Ironically, it was largely the combination of the two that enabled humans to shape costly punishment into numerous low-cost and less detrimental strategies that clearly can promote human cooperation.

Relative Brain and Brain Part Sizes Provide Only Limited Evidence that Machiavellian Behaviour in Cleaner Wrasse Is Cognitively Demanding

It is currently widely accepted that the complexity of a species’ social life is a major determinant of its brain complexity, as predicted by the social brain hypothesis. However, it remains a challenge to explain what social complexity exactly is and what the best corresponding measures of brain anatomy are. Absolute and relative size of the brain and of the neocortex have often been used as a proxy to predict cognitive performance. Here, we apply the logic of the social brain hypothesis to marine cleaning mutualism involving the genus Labroides. These wrasses remove ectoparasites from ‘client’ reef fish. Conflict occurs as wrasse prefer client mucus over ectoparasites, where mucus feeding constitutes cheating. As a result of this conflict, cleaner wrasse show remarkable Machiavellian-like behaviour. Using own data as well as available data from the literature, we investigated whether the general brain anatomy of Labroides provides any indication that their Machiavellian behaviour is associated with a more complex brain. Neither data set provided evidence for an increased encephalisation index compared to other wrasse species. Published data on relative sizes of brain parts in 25 species of the order Perciformes suggests that only the diencephalon is relatively enlarged in Labroides dimidiatus. This part contains various nuclei of the social decision making network. In conclusion, gross brain anatomy yields little evidence for the hypothesis that strategic behaviour in cleaning selects for larger brains, while future research should focus on more detailed aspects like the sizes of specific nuclei as well as their cryoarchitectonic structure and connectivity.

Punitive preferences, monetary incentives and tacit coordination in the punishment of defectors promote cooperation in humans

Peer-punishment is effective in promoting cooperation, but the costs associated with punishing defectors often exceed the benefits for the group. It has been argued that centralized punishment institutions can overcome the detrimental effects of peer-punishment. However, this argument presupposes the existence of a legitimate authority and leaves an unresolved gap in the transition from peer-punishment to centralized punishment. Here we show that the origins of centralized punishment could lie in individuals' distinct ability to punish defectors. In our laboratory experiment, we vary the structure of the punishment situation to disentangle the effects of punitive preferences, monetary incentives, and individual punishment costs on the punishment of defectors. We find that actors tacitly coordinate on the strongest group member to punish defectors, even if the strongest individual incurs a net loss from punishment. Such coordination leads to a more effective and more efficient provision of a cooperative environment than we observe in groups of all equals. Our results show that even an arbitrary assignment of an individual to a focal position in the social hierarchy can trigger the endogenous emergence of more centralized forms of punishment.

Voluntary rewards mediate the evolution of pool punishment for maintaining public goods in large populations

Punishment is a popular tool when governing commons in situations where free riders would otherwise take over. It is well known that sanctioning systems, such as the police and courts, are costly and thus can suffer from those who free ride on other's efforts to maintain the sanctioning systems (second-order free riders). Previous game-theory studies showed that if populations are very large, pool punishment rarely emerges in public good games, even when participation is optional, because of second-order free riders. Here we show that a matching fund for rewarding cooperation leads to the emergence of pool punishment, despite the presence of second-order free riders. We demonstrate that reward funds can pave the way for a transition from a population of free riders to a population of pool punishers. A key factor in promoting the transition is also to reward those who contribute to pool punishment, yet not abstaining from participation. Reward funds eventually vanish in raising pool punishment, which is sustainable by punishing the second-order free riders. This suggests that considering the interdependence of reward and punishment may help to better understand the origins and transitions of social norms and institutions.

Why humans might help strangers

Humans regularly help strangers, even when interactions are apparently unobserved and unlikely to be repeated. Such situations have been simulated in the laboratory using anonymous one-shot games (e.g., prisoner's dilemma) where the payoff matrices used make helping biologically altruistic. As in real-life, participants often cooperate in the lab in these one-shot games with non-relatives, despite that fact that helping is under negative selection under these circumstances. Two broad explanations for such behavior prevail. The "big mistake" or "mismatch" theorists argue that behavior is constrained by psychological mechanisms that evolved predominantly in the context of repeated interactions with known individuals. In contrast, the cultural group selection theorists posit that humans have been selected to cooperate in anonymous one-shot interactions due to strong between-group competition, which creates interdependence among in-group members. We present these two hypotheses before discussing alternative routes by which humans could increase their direct fitness by cooperating with strangers under natural conditions. In doing so, we explain why the standard lab games do not capture real-life in various important aspects. First, asymmetries in the cost of perceptual errors regarding the context of the interaction (one-shot vs. repeated; anonymous vs. public) might have selected for strategies that minimize the chance of making costly behavioral errors. Second, helping strangers might be a successful strategy for identifying other cooperative individuals in the population, where partner choice can turn strangers into interaction partners. Third, in contrast to the assumptions of the prisoner's dilemma model, it is possible that benefits of cooperation follow a non-linear function of investment. Non-linear benefits result in negative frequency dependence even in one-shot games. Finally, in many real-world situations individuals are able to parcel investments such that a one-shot interaction is turned into a repeated game of many decisions.

Sanctions as honest signals--the evolution of pool punishment by public sanctioning institutions

In many species, mutual cooperation is stabilized by forms of policing and peer punishment: if cheaters are punished, there is a strong selective pressure to cooperate. Most human societies have complemented, and sometimes even replaced, such peer punishment mechanisms with pool punishment, where punishment is outsourced to central institutions such as the police. Even before free-riding occurs, such institutions require investments, which could serve as costly signals. Here, we show with a game theoretical model that this signaling effect in turn can be crucial for the evolution of punishment institutions: In the absence of such signals, pool punishment is only stable with second-order punishment and can only evolve when individuals have the freedom not to take part in any interaction. With such signals, individuals can opportunistically adjust their behavior, which promotes the evolution of stable pool punishment even in situations where no one can stand aside. Thus, the human propensity to react opportunistically to credible punishment threats is often sufficient to establish stable punishment institutions and to maintain high levels of cooperation.

Rewards and the evolution of cooperation in public good games

Properly coordinating cooperation is relevant for resolving public good problems, such as clean energy and environmental protection. However, little is known about how individuals can coordinate themselves for a certain level of cooperation in large populations of strangers. In a typical situation, a consensus-building process rarely succeeds, owing to a lack of face and standing. The evolution of cooperation in this type of situation is studied here using threshold public good games, in which cooperation prevails when it is initially sufficient, or otherwise it perishes. While punishment is a powerful tool for shaping human behaviours, institutional punishment is often too costly to start with only a few contributors, which is another coordination problem. Here, we show that whatever the initial conditions, reward funds based on voluntary contribution can evolve. The voluntary reward paves the way for effectively overcoming the coordination problem and efficiently transforms freeloaders into cooperators with a perceived small risk of collective failure.

Democratic decisions establish stable authorities that overcome the paradox of second-order punishment

Individuals usually punish free riders but refuse to sanction those who cooperate but do not punish. This missing second-order peer punishment is a fundamental problem for the stabilization of cooperation. To solve this problem, most societies today have implemented central authorities that punish free riders and tax evaders alike, such that second-order punishment is fully established. The emergence of such stable authorities from individual decisions, however, creates a new paradox: it seems absurd to expect individuals who do not engage in second-order punishment to strive for an authority that does. Herein, we provide a mathematical model and experimental results from a public goods game where subjects can choose between a community with and without second-order punishment in two different ways. When subjects can migrate continuously to either community, we identify a bias toward institutions that do not punish tax evaders. When subjects have to vote once for all rounds of the game and have to accept the decision of the majority, they prefer a society with second-order punishment. These findings uncover the existence of a democracy premium. The majority-voting rule allows subjects to commit themselves and to implement institutions that eventually lead to a higher welfare for all.

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.

Individual differences in foraging strategies of parasitic sabre-tooth blennies

Originally, evolutionary game theory typically predicted that optimal behaviour in a given situation is uniform or bimodal. However, the growing evidence that animals behave more variably while individuals may differ consistently in their behaviour, has led to the development of models that predict a distribution of strategies. Here we support the importance of such models in a study on a coral reef fish host–parasite system. Parasitic blennies (Plagiotremus sp.) regularly attack other fishes to bite off scales and mucus. Individuals of some victim species react to being bitten with punishing the parasite through aggressive chasing. Our field observations and laboratory experiments show that individual blennies differ markedly in how they incorporate being punished into their foraging decisions. We discuss how these differences may affect the payoff structure and hence the net effect of punishment on punishers and on the appearance of a public good for look-alikes.

An economic experiment reveals that humans prefer pool punishment to maintain the commons

Punishment can stabilize costly cooperation and ensure the success of a common project that is threatened by free-riders. Punishment mechanisms can be classified into pool punishment, where the punishment act is carried out by a paid third party, (e.g. a police system or a sheriff), and peer punishment, where the punishment act is carried out by peers. Which punishment mechanism is preferred when both are concurrently available within a society? In an economic experiment, we show that the majority of subjects choose pool punishment, despite being costly even in the absence of defectors, when second-order free-riders, cooperators that do not punish, are also punished. Pool punishers are mutually enforcing their support for the punishment organization, stably trapping each other. Our experimental results show how organized punishment could have displaced individual punishment in human societies.

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.