The evolution of antisocial punishment in optional public goods games

Prosocial punishment bots breed social punishment in human players

Prosocial punishment, an important factor to stabilize cooperation in social dilemma games, often faces challenges like second-order free-riders-who cooperate but avoid punishing to save costs-and antisocial punishers, who defect and retaliate against cooperators. Addressing these challenges, our study introduces prosocial punishment bots that consistently cooperate and punish free-riders. Our findings reveal that these bots significantly promote the emergence of prosocial punishment among normal players due to their 'sticky effect'-an unwavering commitment to cooperation and punishment that magnetically attracts their opponents to emulate this strategy. Additionally, we observe that the prevalence of prosocial punishment is greatly enhanced when normal players exhibit a tendency to follow a 'copying the majority' strategy, or when bots are strategically placed in high-degree nodes within scale-free networks. Conversely, bots designed for defection or antisocial punishment diminish overall cooperation levels. This stark contrast underscores the critical role of strategic bot design in enhancing cooperative behaviours in human/AI interactions. Our findings open new avenues in evolutionary game theory, demonstrating the potential of human-machine collaboration in solving the conundrum of punishment.

Antisocial peer exclusion does not eliminate the effectiveness of prosocial peer exclusion in structured populations

While prosocial exclusion has been proposed as a mechanism to maintain cooperation in one-shot social dilemma games, the evolution of prosocial peer exclusion in response to the threat of antisocial peer exclusion, particularly in structured populations, remains insufficiently understood. In this study, we employ an extended spatial public goods game to investigate the evolution of prosocial peer exclusion and its impact on cooperation in the presence of both prosocial and antisocial peer exclusion. Our model encompasses four primary strategies: traditional cooperation and defection, prosocial peer exclusion targeting defectors, and antisocial peer exclusion targeting cooperators. Our findings illuminate that the presence of antisocial peer exclusion significantly disrupts network reciprocity and suppresses cooperation. However, when coexisting with prosocial peer exclusion, it does not undermine the latter's efficacy in upholding cooperation, except in scenarios with low exclusion costs Unlike the cooperation-sustaining cyclic dominance pattern observed in the exclusive presence of prosocial peer exclusion, the co-presence of prosocial and antisocial peer exclusion gives rise to more intricate pathways for maintaining cooperation. These pathways include cyclic dominance involving traditional cooperation, prosocial peer exclusion, and antisocial peer exclusion, or a similar pattern involving traditional defection and the two exclusion strategies, or even cyclic dominance among all four strategies. In essence, our study enhances the theoretical framework concerning the effectiveness of the prosocial exclusion strategy, contributing to a more comprehensive understanding of its dynamics.

Reducing global inequality increases local cooperation: a simple model of group selection with a global externality

Group-structured models often explain the evolution of prosocial activities in terms of selection acting at both individual and group levels. Such models do not typically consider how individuals' behaviours may have consequences beyond the boundaries of their groups. However, many behaviours affect global environmental variables, including climate change and ecosystem fragility. Against this background, we propose a simple model of multi-level selection in the presence of global externalities. In our model, group members can cooperate in a social dilemma with the potential for group-level benefits. The actions of cooperators also have global consequences, which can be positive (a global good) or negative (a global bad). We use simulations to consider scenarios in which the effects of the global externality either are evenly distributed, or have stronger influences on either the rich or the poor. We find that the global externality promotes the evolution of cooperation only if it either disproportionately benefits the poor or disproportionately reduces the payoffs of the rich. If the global externality primarily harms the poor, it undermines the evolution of prosocial behaviour. Understanding this effect is important given concerns that poorer households are more vulnerable to climate change impacts. This article is part of the theme issue 'Evolution and sustainability: gathering the strands for an Anthropocene synthesis'.

Tax thresholds yield multiple optimal cooperation levels in the spatial public goods game

Income redistribution, which involves transferring income from certain individuals to others, plays a crucial role in human societies. Previous research has indicated that tax-based redistribution can promote cooperation by enhancing incentives for cooperators. In such a tax system, all individuals, irrespective of their income levels, contribute to the tax system, and the tax revenue is subsequently redistributed to everyone. In this study, we relax this assumption by introducing a tax threshold, signifying that only individuals with incomes exceeding the threshold will be subject to taxation. In particular, we employ the spatial public goods game to investigate the influence of tax rates-the percentage of income allocated to tax-and tax thresholds, which determine the income level at which individuals become taxable, on the evolution of cooperation. Our extensive numerical simulations disclose that tax thresholds produce complex outcomes for the evolution of cooperation, depending on tax rates. Notably, at low tax rates (i.e., below 0.41), as the tax threshold increases, discontinuous phase transitions in cooperation performance suggest the presence of multiple intervals of effective tax thresholds that promote peak cooperation levels. Nevertheless, irrespective of the chosen tax rate, once the tax threshold surpasses a critical threshold, the redistribution mechanism fails, causing the collapse of cooperation. Evolutionary snapshots show that self-organized redistribution forms an intermediary layer on the peripheries of cooperative clusters, effectively shielding cooperators from potential defectors. Quantitative analyses shed light on how self-organized redistribution narrows the income gap between cooperators and defectors through precise identification of tax-exempt entities, thereby amplifying the cooperative advantage. Collectively, these findings enhance our comprehension of how income redistribution influences cooperation, highlighting the pivotal role of tax thresholds.

Nonlinear eco-evolutionary games with global environmental fluctuations and local environmental feedbacks

Environmental changes play a critical role in determining the evolution of social dilemmas in many natural or social systems. Generally, the environmental changes include two prominent aspects: the global time-dependent fluctuations and the local strategy-dependent feedbacks. However, the impacts of these two types of environmental changes have only been studied separately, a complete picture of the environmental effects exerted by the combination of these two aspects remains unclear. Here we develop a theoretical framework that integrates group strategic behaviors with their general dynamic environments, where the global environmental fluctuations are associated with a nonlinear factor in public goods game and the local environmental feedbacks are described by the 'eco-evolutionary game'. We show how the coupled dynamics of local game-environment evolution differ in static and dynamic global environments. In particular, we find the emergence of cyclic evolution of group cooperation and local environment, which forms an interior irregular loop in the phase plane, depending on the relative changing speed of both global and local environments compared to the strategic change. Further, we observe that this cyclic evolution disappears and transforms into an interior stable equilibrium when the global environment is frequency-dependent. Our results provide important insights into how diverse evolutionary outcomes could emerge from the nonlinear interactions between strategies and the changing environments.

The future of theoretical evolutionary game theory

Evolutionary game theory is a truly interdisciplinary subject that goes well beyond the limits of biology. Mathematical minds get hooked up in simple models for evolution and often gradually move into other parts of evolutionary biology or ecology. Social scientists realize how much they can learn from evolutionary thinking and gradually transfer insight that was originally generated in biology. Computer scientists can use their algorithms to explore a new field where machines not only learn from the environment, but also from each other. The breadth of the field and the focus on a few very popular issues, such as cooperation, comes at a price: several insights are re-discovered in different fields under different labels with different heroes and modelling traditions. For example, reciprocity or spatial structure are treated differently. Will we continue to develop things in parallel? Or can we converge to a single set of ideas, a single tradition and eventually a single software repository? Or will these fields continue to cross-fertilize each other, learning from each other and engaging in a constructive exchange between fields? Ultimately, the popularity of evolutionary game theory rests not only on its explanatory power, but also on the intuitive character of its models. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Complex evolutionary interactions in multiple populations

In competitive settings that entail several populations, individuals often engage in intra- and interpopulation interactions that determine their fitness and evolutionary success. With this simple motivation, we here study a multipopulation model where individuals engage in group interactions within their own population and in pairwise interactions with individuals from different populations. We use the evolutionary public goods game and the prisoner's dilemma game to describe these group and pairwise interactions, respectively. We also take into account asymmetry in the extent to which group and pairwise interactions determine the fitness of individuals. We find that interactions across multiple populations reveal new mechanisms through which the evolution of cooperation can be promoted, but this depends on the level of interaction asymmetry. If inter- and intrapopulation interactions are symmetric, the sole presence of multiple populations promotes the evolution of cooperation. Asymmetry in the interactions can further promote cooperation at the expense of the coexistence of the competing strategies. An in-depth analysis of the spatiotemporal dynamics reveals loop-dominated structures and pattern formation that can explain the various evolutionary outcomes. Thus, complex evolutionary interactions in multiple populations reveal an intricate interplay between cooperation and coexistence, and they also open up the path toward further explorations of multipopulation games and biodiversity.

The evolution of universal cooperation

Humans work together in groups to tackle shared problems and contribute to local club goods that benefit other group members. Whereas benefits from club goods remain group bound, groups are often nested in overarching collectives that face shared problems like pandemics or climate change. Such challenges require individuals to cooperate across group boundaries, raising the question how cooperation can transcend beyond confined groups. Here, we show how frequent intergroup interactions allow groups to transition from group-bound to universal cooperation. With frequent intergroup interactions, reciprocity of cooperative acts permeates group boundaries and enables the evolution of universal cooperation. As soon as intergroup interactions take place frequently, people start to selectively reward cooperation aimed at benefitting everyone, irrespective of their group membership. Simulations further show that it becomes more difficult to overcome group-bound cooperation when populations are fragmented into many small groups. Our findings reveal important prerequisites for the evolution of universal cooperation.

Cooperation without punishment

A fundamental question in social and biological sciences is whether self-governance is possible when individual and collective interests are in conflict. Free riding poses a major challenge to self-governance, and a prominent solution to this challenge has been altruistic punishment. However, this solution is ineffective when counter-punishments are possible and when social interactions are noisy. We set out to address these shortcomings, motivated by the fact that most people behave like conditional cooperators-individuals willing to cooperate if a critical number of others do so. In our evolutionary model, the population contains heterogeneous conditional cooperators whose decisions depend on past cooperation levels. The population plays a repeated public goods game in a moderately noisy environment where individuals can occasionally commit mistakes in their cooperative decisions and in their imitation of the role models' strategies. We show that, under moderate levels of noise, injecting a few altruists into the population triggers positive reciprocity among conditional cooperators, thereby providing a novel mechanism to establish stable cooperation. More broadly, our findings indicate that self-governance is possible while avoiding the detrimental effects of punishment, and suggest that society should focus on creating a critical amount of trust to harness the conditional nature of its members.

Authority or Autonomy? Exploring Interactions between Central and Peer Punishments in Risk-Resistant Scenarios

Game theory provides a powerful means to study human cooperation and better understand cooperation-facilitating mechanisms in general. In classical game-theoretic models, an increase in group cooperation constantly increases people's gains, implying that individual gains are a continuously varying function of the cooperation rate. However, this is inconsistent with the increasing number of risk-resistant scenarios in reality. A risk-resistant scenario means once a group does not successfully resist the risk, all individuals lose their resources, such as a community coping with COVID-19 and a village resisting a flood. In other words, individuals' gains are segmented about the collaboration rate. This paper builds a risk-resistant model to explore whether punishment still promotes collaboration when people resist risk. The results show that central and peer punishments can both encourage collaboration but with different characteristics under different risk-resistant scenarios. Specifically, central punishment constrains the collaboration motivated by peer punishment regardless of risk, while peer punishment limits the collaboration induced by central punishment only when the risk is high. Our findings provide insights into the balance between peer punishment from public autonomy and central punishment from central governance, and the proposed model paves the way for the development of richer risk-resistant models.

Replicator dynamics of public goods games with global exclusion

Studies to date on the role of social exclusion in public cooperation have mainly focused on the peer or pool sanctioning types of excluding free-riders from the share of common goods. However, the exclusive behaviors are not necessarily performed by individuals or local organizations but may rather be implemented by a centralized enforcement institution at a global scale. Besides, previous modeling methods of either peer or pool exclusion often presuppose some particular forms of feedback between the individual or collective efforts and the efficiency of social exclusion and, therefore, cannot comprehensively evaluate their effects on the evolution of cooperation in the social dilemma situations. Here, we construct a general model of global exclusion by considering the successful construction of the centralized exclusive institution as an arbitrary non-decreasing and smooth function of the collective efforts made by the global excluders and then theoretically analyze its potential impacts in the replicator dynamics of the public goods game. Interestingly, we have shown that, despite the presence of both the first- and second-order free-riding problems, global exclusion can indeed lead to the emergence or even stabilization of public cooperation without the support of any other evolutionary mechanism. In addition, we have also observed rich dynamical behaviors, such as the occurrence of a global or local family of neutrally stable closed orbits revolving around a nonlinear center or the existence of stable heteroclinic cycles between defectors, cooperators as well as global excluders, which give rise to a classification of up to 21 different phases.

The probabilistic pool punishment proportional to the difference of payoff outperforms previous pool and peer punishment

The public goods game is a multiplayer version of the prisoner’s dilemma game. In the public goods game, punishment on defectors is necessary to encourage cooperation. There are two types of punishment: peer punishment and pool punishment. Comparing pool punishment with peer punishment, pool punishment is disadvantageous in comparison with peer punishment because pool punishment incurs fixed costs especially if second-order free riders (those who invest in public goods but do not punish defectors) are not punished. In order to eliminate such a flaw of pool punishment, this study proposes the probabilistic pool punishment proportional to the difference of payoff. In the proposed pool punishment, each punisher pays the cost to the punishment pool with the probability proportional to the difference of payoff between his/her payoff and the average payoff of his/her opponents. Comparing the proposed pool punishment with previous pool and peer punishment, in pool punishment of previous studies, cooperators who do not punish defectors become dominant instead of pool punishers with fixed costs. However, in the proposed pool punishment, more punishers and less cooperators coexist, and such state is more robust against the invasion of defectors due to mutation than those of previous pool and peer punishment. The average payoff is also comparable to peer punishment of previous studies.

Institutional incentives for the evolution of committed cooperation: ensuring participation is as important as enhancing compliance

Both conventional wisdom and empirical evidence suggest that arranging a prior commitment or agreement before an interaction takes place enhances the chance of reaching mutual cooperation. Yet it is not clear what mechanisms might underlie the participation in and compliance with such a commitment, especially when participation is costly and non-compliance can be profitable. Here, we develop a theory of participation and compliance with respect to an explicit commitment formation process and to institutional incentives where individuals, at first, decide whether or not to join a cooperative agreement to play a one-shot social dilemma game. Using a mathematical model, we determine whether and when participating in a costly commitment, and complying with it, is an evolutionarily stable strategy, resulting in high levels of cooperation. We show that, given a sufficient budget for providing incentives, rewarding of commitment compliant behaviours better promotes cooperation than punishment of non-compliant ones. Moreover, by sparing part of this budget for rewarding those willing to participate in a commitment, the overall level of cooperation can be significantly enhanced for both reward and punishment. Finally, the presence of mistakes in deciding to participate favours evolutionary stability of commitment compliance and cooperation.

Reputation and punishment sustain cooperation in the optional public goods game

Cooperative behaviour has been extensively studied as a choice between cooperation and defection. However, the possibility to not participate is also frequently available. This type of problem can be studied through the optional public goods game. The introduction of the 'Loner' strategy' allows players to withdraw from the game, which leads to a cooperator-defector-loner cycle. While pro-social punishment can help increase cooperation, anti-social punishment-where defectors punish cooperators-causes its downfall in both experimental and theoretical studies. In this paper, we introduce social norms that allow agents to condition their behaviour to the reputation of their peers. We benchmark this with respect both to the standard optional public goods game and to the variant where all types of punishment are allowed. We find that a social norm imposing a more moderate reputational penalty for opting out than for defecting increases cooperation. When, besides reputation, punishment is also possible, the two mechanisms work synergically under all social norms that do not assign to loners a strictly worse reputation than to defectors. Under this latter set-up, the high levels of cooperation are sustained by conditional strategies, which largely reduce the use of pro-social punishment and almost completely eliminate anti-social punishment. This article is part of the theme issue 'The language of cooperation: reputation and honest signalling'.

Decoupling cooperation and punishment in humans shows that punishment is not an altruistic trait

Economic experiments have suggested that cooperative humans will altruistically match local levels of cooperation (conditional cooperation) and pay to punish non-cooperators (altruistic punishment). Evolutionary models have suggested that if altruists punish non-altruists this could favour the evolution of costly helping behaviours (cooperation) among strangers. An often-key requirement is that helping behaviours and punishing behaviours form one single conjoined trait (strong reciprocity). Previous economics experiments have provided support for the hypothesis that punishment and cooperation form one conjoined, altruistically motivated, trait. However, such a conjoined trait may be evolutionarily unstable, and previous experiments have confounded a fear of being punished with being surrounded by cooperators, two factors that could favour cooperation. Here, we experimentally decouple the fear of punishment from a cooperative environment and allow cooperation and punishment behaviour to freely separate (420 participants). We show, that if a minority of individuals is made immune to punishment, they (i) learn to stop cooperating on average despite being surrounded by high levels of cooperation, contradicting the idea of conditional cooperation and (ii) often continue to punish, 'hypocritically', showing that cooperation and punishment do not form one, altruistically motivated, linked trait.

Evolution of prosocial punishment in unstructured and structured populations and in the presence of antisocial punishment

A large body of empirical evidence suggests that altruistic punishment abounds in human societies. Based on such evidence, it is suggested that punishment serves an important role in promoting cooperation in humans and possibly other species. However, as punishment is costly, its evolution is subject to the same problem that it tries to address. To suppress this so-called second-order free-rider problem, known theoretical models on the evolution of punishment resort to one of the few established mechanisms for the evolution of cooperation. This leaves the question of whether altruistic punishment can evolve and give rise to the evolution of cooperation in the absence of such auxiliary cooperation-favoring mechanisms unaddressed. Here, by considering a population of individuals who play a public goods game, followed by a public punishing game, introduced here, we show that altruistic punishment indeed evolves and promotes cooperation in the absence of a cooperation-favoring mechanism. In our model, the punishment pool is considered a public resource whose resources are used for punishment. We show that the evolution of a punishing institution is facilitated when resources in the punishment pool, instead of being wasted, are used to reward punishers when there is nobody to punish. Besides, we show that higher returns to the public resource or punishment pool facilitate the evolution of prosocial instead of antisocial punishment. We also show that an optimal cost of investment in the punishment pool facilitates the evolution of prosocial punishment. Finally, our analysis shows that being close to a physical phase transition facilitates the evolution of altruistic punishment.

Consensus towards Partially Cooperative Strategies in Self-Regulated Evolutionary Games on Networks

Cooperation is widely recognized to be fundamental for the well-balanced development of human societies. Several different approaches have been proposed to explain the emergence of cooperation in populations of individuals playing the Prisoner’s Dilemma game, characterized by two concurrent natural mechanisms: the temptation to defect and the fear to be betrayed by others. Few results are available for analyzing situations where only the temptation to defect (Chicken game) or the fear to be betrayed (Stag-Hunt game) is present. In this paper, we analyze the emergence of full and partial cooperation for these classes of games. We find the conditions for which these Nash equilibria are asymptotically stable, and we show that the partial one is also globally stable. Furthermore, in the Chicken and Stag-Hunt games, partial cooperation has been found to be more rewarding than the full one of the Prisoner’s Dilemma game. This result highlights the importance of such games for understanding and sustaining different levels of cooperation in social networks.

Trust-based partner switching among partitioned regions promotes cooperation in public goods game

In this paper, the coevolution mechanism of trust-based partner switching among partitioned regions on an adaptive network is studied. We investigate a low-information approach to building trust and cooperation in public goods games. Unlike reputation, trust scores are only given to players by those with whom they have a relationship in the game, depending on the game they play together. A player's trust score for a certain neighbor is given and known by that player only. Players can adjust their connections to neighbors with low trust scores by switching their partners to other players. When switching partners, players divide other nodes in the network into three regions: immediate neighbors as the known region, indirectly connected second-order neighbors as the intermediate region, and other nodes as the unknown region. Such choices and compartmentalization often occur in global and regional economies. Our results show that preference for switching to partners in the intermediate region is not conducive to spreading cooperation, while random selection has the disadvantage of protecting the cooperator. However, selecting new partners in the remaining two regions based on the average trust score of the known region performs well in both protecting partners and finding potential cooperators. Meanwhile, by analyzing the parameters, we find that the influence of vigilance increasing against unsatisfactory behavior on evolution direction depends on the level of cooperation reward.

Evolutionary Dynamics of Gig Economy Labor Strategies under Technology, Policy and Market Influence

The emergence of the modern gig economy introduces a new set of employment considerations for firms and laborers that include various trade-offs. With a game-theoretical approach, we examine the influences of technology, policy and markets on firm and worker preferences for gig labor. Theoretically, we present new conceptual extensions to the replicator equation and model oscillating dynamics in two-player asymmetric bi-matrix games with time-evolving environments, introducing concepts of the attractor arc, trapping zone and escape. While canonical applications of evolutionary game theory focus on the evolutionary stable strategy, our model assumes that the system exhibits oscillatory dynamics and can persist for long temporal intervals in a pseudo-stable state. We demonstrate how changing market conditions result in distinct evolutionary patterns across labor economies. Informing tensions regarding the future of this new employment category, we present a novel payoff framework to analyze the role of technology on the growth of the gig economy. Regarding governance, we explore regulatory implications within the gig economy, demonstrating how intervals of lenient and strict policy alter firm and worker sensitivities between gig and employee labor strategies. Finally, we establish an aggregate economic framework to explain how technology, policy and market environments engage in an interlocking dance, a balancing act, to sustain the observable co-existence of gig and employee labor strategies.

Understanding evolutionary and ecological dynamics using a continuum limit

Continuum limits in the form of stochastic differential equations are typically used in theoretical population genetics to account for genetic drift or more generally, inherent randomness of the model. In evolutionary game theory and theoretical ecology, however, this method is used less frequently to study demographic stochasticity. Here, we review the use of continuum limits in ecology and evolution. Starting with an individual-based model, we derive a large population size limit, a (stochastic) differential equation which is called continuum limit. By example of the Wright-Fisher diffusion, we outline how to compute the stationary distribution, the fixation probability of a certain type, and the mean extinction time using the continuum limit. In the context of the logistic growth equation, we approximate the quasi-stationary distribution in a finite population.

Cooperation in spatial public good games depends on the locality effects of game, adaptation, and punishment

Despite intensive studies on the evolution of cooperation in spatial public goods games, there have been few investigations into locality effects in interaction games, adaptation, and punishment. Here we analyze locality effects using an agent-based model of a regular graph. Our simulation shows that a situation containing a local game, local punishment, and global adaptation leads to the most robustly cooperative regime. Further, we show an interesting feature in local punishment. Previous studies showed that a local game and global adaptation are likely to generate cooperation. However, they did not consider punishment. We show that if local punishment is introduced in spatial public goods games, a situation satisfying either local game or local adaptation is likely to generate cooperation. We thus propose two principles. One is if interactions in games can be restricted locally, it is likely to generate cooperation independent of the interaction situations on punishment and adaptation. The other is if the games must be played globally, a cooperative regime requires both local punishment and local adaptation.

Egoistic punishment outcompetes altruistic punishment in the spatial public goods game

The evolution of costly punishment is a puzzle due to cooperators’ second-order free-riding. Previous studies have proposed many solutions mainly focused on reducing the punishment cost or punishing second-order free riders directly or indirectly. We attempt to explain this confusion from the perspective of punishment motivation, which is why the punisher is willing to pay the cost. The answer is that the punisher is egoistic. Egoistic punishment aims to protect punishers’ own cooperative benefits shared by the defectors. In such case, egoistic punishers would pay a cost in punishing defectors and retrieve lost payoffs from defectors. Here, we examined the evolution and performance of egoistic punishment and compared it with typical altruistic punishment using classic peer-punishment and pool-punishment modes. Results showed egoistic punishment can evolve and effectively promote cooperation within a large parameter range, whether in a well-mixed or structured population, or through peer-punishment or pool-punishment modes. This result is also robust to different strategy-updating rules. The evolution under the pool-punishment mechanism is more complicated. The influence of parameters is counter-intuitive because of cycle dominance; namely, the cost is the key factor to control the level of cooperation and the fine determines the ratio of the punishers and cooperators. Compared with altruistic punishment, egoistic punishment can promote cooperation in a lower-fine and higher-cost area, especially in the pool punishment mode, and the egoistic punishers have stronger survivability. Egoistic punishers represent the natural fairness in a social system. Results revealed that focusing on individual equity can significantly promote collective cooperation. This study provides another explanation for the evolution of costly punishment.

Voluntary restrictions on self-reliance increase cooperation and mitigate wealth inequality

Humans are considered a highly cooperative species. Through cooperation, we can tackle shared problems like climate change or pandemics and cater for shared needs like shelter, mobility, or healthcare. However, cooperation invites free-riding and can easily break down. Maybe because of this reason, societies also enable individuals to solve shared problems individually, like in the case of private healthcare plans or private retirement planning. Such "self-reliance" allows individuals to avoid problems related to public goods provision, like free-riding or underprovision, and decreases social interdependence. However, not everyone can equally afford to be self-reliant, and amid shared problems, self-reliance may lead to conflicts within groups on how to solve shared problems. In two preregistered studies, we investigate how the ability of self-reliance influences collective action and cooperation. We show that self-reliance crowds out cooperation and exacerbates inequality, especially when some heavily depend on collective action while others do not. However, we also show that groups are willing to curtail their ability of self-reliance. When given the opportunity, groups overwhelmingly vote in favor of abolishing individual solutions to shared problems, which, in turn, increases cooperation and decreases inequality, particularly between group members that differ in their ability to be self-reliant. The support for such endogenously imposed interdependence, however, reduces when individual solutions become more affordable, resonating with findings of increased individualism in wealthier societies and suggesting a link between wealth inequality and favoring individual independence and freedom over communalism and interdependence.

Self-reliance crowds out group cooperation and increases wealth inequality

Humans establish public goods to provide for shared needs like safety or healthcare. Yet, public goods rely on cooperation which can break down because of free-riding incentives. Previous research extensively investigated how groups solve this free-rider problem but ignored another challenge to public goods provision. Namely, some individuals do not need public goods to solve the problems they share with others. We investigate how such self-reliance influences cooperation by confronting groups in a laboratory experiment with a safety problem that could be solved either cooperatively or individually. We show that self-reliance leads to a decline in cooperation. Moreover, asymmetries in self-reliance undermine social welfare and increase wealth inequality between group members. Less dependent group members often choose to solve the shared problem individually, while more dependent members frequently fail to solve the problem, leaving them increasingly poor. While self-reliance circumvents the free-rider problem, it complicates the governing of the commons.

Cooperation among humans is threatened by the free-rider problem. Here the authors identify another challenge to human cooperation: self-reliance, the ability to solve shared problems individually. The experiment reveals that self-reliance crowds out cooperation and increases wealth inequality.

The Singaporean model in public goods dilemmas with benevolent leaders and bribery

Public goods dilemmas are at the heart of some of the greatest challenges of our time, including climate inaction, growing inequality, and the overuse of natural resources. The public goods game in which cooperators contribute to a common pool that is then shared equally with defectors who contribute nothing captures the gist of the problem. Cooperators therefore cannot prevail, which ultimately leads to the tragedy of the commons. Actions such as punishment, rewards, and exclusion have been shown to help, but they are costly, therefore rendering cooperators second-order free-riders due to their lack of participation in these actions. In the search for a remedy, we study the public goods game with benevolent leaders who, at a personal cost, have the ability to exclude defectors from using common pool resources. We also consider bribers who can pay the leaders to relax their exclusion efforts. In a traditional setting, this setup yields the standard second-order free-rider problem, where, ironically, the leaders are overcome by cooperators, who then themselves succumb to defectors. We show, however, that the Singaporean model - where a leader's payoff is determined not only by the regular sharing income from the firm production but also by the success of gross firm production as an incentive - can resolve the second-order free-rider problem. We also show that the detrimental effect of bribery can always be, no matter how high the bribe, held in check as long as the number of individuals engaged in this activity is low compared to the number of benevolent leaders. Otherwise, an abrupt transition to a cooperator-less state becomes unavoidable. We discuss the implications of our research for designing successful cooperation and anti-corruption strategies in public goods dilemmas.

A Review of Theoretical Studies on Indirect Reciprocity

Despite the accumulation of research on indirect reciprocity over the past 30 years and the publication of over 100,000 related papers, there are still many issues to be addressed. Here, we look back on the research that has been done on indirect reciprocity and identify the issues that have been resolved and the ones that remain to be resolved. This manuscript introduces indirect reciprocity in the context of the evolution of cooperation, basic models of social dilemma situations, the path taken in the elaboration of mathematical analysis using evolutionary game theory, the discovery of image scoring norms, and the breakthroughs brought about by the analysis of the evolutionary instability of the norms. Moreover, it presents key results obtained by refining the assessment function, resolving the punishment dilemma, and presenting a complete solution to the social dilemma problem. Finally, it discusses the application of indirect reciprocity in various disciplines.

Self-regulation versus social influence for promoting cooperation on networks

Cooperation is a relevant and controversial phenomenon in human societies. Indeed, although it is widely recognized essential for tackling social dilemmas, finding suitable policies for promoting cooperation can be arduous and expensive. More often, it is driven by pre-established schemas based on norms and punishments. To overcome this paradigm, we highlight the interplay between the influence of social interactions on networks and spontaneous self-regulating mechanisms on individuals behavior. We show that the presence of these mechanisms in a prisoner's dilemma game, may oppose the willingness of individuals to defect, thus allowing them to behave cooperatively, while interacting with others and taking conflicting decisions over time. These results are obtained by extending the Evolutionary Game Equations over Networks to account for self-regulating mechanisms. Specifically, we prove that players may partially or fully cooperate whether self-regulating mechanisms are sufficiently stronger than social pressure. The proposed model can explain unconditional cooperation (strong self-regulation) and unconditional defection (weak self-regulation). For intermediate self-regulation values, more complex behaviors are observed, such as mutual defection, recruiting (cooperate if others cooperate), exploitation of cooperators (defect if others cooperate) and altruism (cooperate if others defect). These phenomena result from dynamical transitions among different game structures, according to changes of system parameters and cooperation of neighboring players. Interestingly, we show that the topology of the network of connections among players is crucial when self-regulation, and the associated costs, are reasonably low. In particular, a population organized on a random network with a Scale-Free distribution of connections is more cooperative than on a network with an Erdös-Rényi distribution, and, in turn, with a regular one. These results highlight that social diversity, encoded within heterogeneous networks, is more effective for promoting cooperation.

The competitive advantage of institutional reward

Sustaining cooperation among unrelated individuals is a fundamental challenge in biology and the social sciences. In human society, this problem can be solved by establishing incentive institutions that reward cooperators and punish free-riders. Most of the previous studies have focused on which incentives promote cooperation best. However, a higher cooperation level does not always imply higher group fitness, and only incentives that lead to higher fitness can survive in social evolution. In this paper, we compare the efficiencies of three types of institutional incentives, namely, reward, punishment, and a mixture of reward and punishment, by analysing the group fitness at the stable equilibria of evolutionary dynamics. We find that the optimal institutional incentive is sensitive to decision errors. When there is no error, a mixture of reward and punishment can lead to high levels of cooperation and fitness. However, for intermediate and large errors, reward performs best, and one should avoid punishment. The failure of punishment is caused by two reasons. First, punishment cannot maintain a high cooperation level. Second, punishing defectors almost always reduces the group fitness. Our findings highlight the role of reward in human cooperation. In an uncertain world, the institutional reward is not only effective but also efficient.

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.

Cooperator-driven and defector-driven punishments: How do they influence cooperation?

Economic studies have shown that there are two types of regulation schemes which can be considered as a vital part of today's global economy: self-regulation enforced by self-regulation organizations to govern industry practices and government regulation which is considered as another scheme to sustain corporate adherence. An outstanding problem of particular interest is to understand quantitatively the role of these regulation schemes in evolutionary dynamics. Typically, punishment usually occurs for enforcement of regulations. Taking into account both types of punishments to influence the regulations, we develop a game model where six evolutionary situations with corresponding combinations of strategies are considered. Furthermore, a semianalytical method is developed to allow us to give accurate estimations of the boundaries between the phases of full defection and nondefection. We find that, associated with the evolutionary dynamics, for an infinite well-mixed population, the mix of both punishments performs better than one punishment alone in promoting public cooperation, but for a networked population the cooperator-driven punishment turns out to be a better choice. We also reveal the monotonic facilitating effects of the synergy effect, punishment fine, and feedback sensitivity on the public cooperation for an infinite well-mixed population. Conversely, for a networked population an optimal intermediate range of feedback sensitivity is needed to best promote punishers' populations. Overall, a networked structure is overall more favorable for punishers and further for public cooperation, because of both network reciprocity and mutualism between punishers and cooperators who do not punish defectors. We provide physical understandings of the observed phenomena, through a detailed statistical analysis of frequencies of different strategies and spatial pattern formations in different evolution situations. These results provide valuable insights into how to select and enforce suitable regulation measures to let public cooperation remain prevalent, which has potential implications not only for self-regulation, but also for other topics in economics and social science.

Cross-scale cooperation enables sustainable use of a common-pool resource

In social-ecological systems (SESs), social and biophysical dynamics interact within and between the levels of organization at multiple spatial and temporal scales. Cross-scale interactions (CSIs) are interdependences between processes at different scales, generating behaviour unpredictable at single scales. Understanding CSIs is important for improving SES governance, but they remain understudied. Theoretical models are needed that capture essential features while being simple enough to yield insights into mechanisms. In a stylized model, we study CSIs in a two-level system of weakly interacting communities harvesting a common-pool resource. Community members adaptively conform to, or defect from, a norm of socially optimal harvesting, enforced through social sanctioning both within and between communities. We find that each subsystem's dynamics depend sensitively on the other despite interactions being much weaker between subsystems than within them. When interaction is purely biophysical, stably high cooperation in one community can cause cooperation in the other to collapse. However, even weak social interaction can prevent the collapse of cooperation and instead cause collapse of defection. We identify conditions under which subsystem-level cooperation produces desirable system-level outcomes. Our findings expand evidence that collaboration is important for sustainably managing shared resources, showing its importance even when resource sharing and social relationships are weak.

The evolution of cooperation in spatial public goods game with conditional peer exclusion

Social exclusion can prevent free riders from participating in social activities and deprive them of sharing cooperative benefits, which is an effective mechanism for the evolution of cooperation. However, traditional peer-exclusion strategies are unconditional, and as long as there are defectors in the group, they will pay a cost to exclude the defectors. In reality, one of the reasons for the complexity of these strategies is that individuals may react differently depending on the environment in which they are located. Based on this consideration, we introduce a kind of conditional peer-exclusion strategy in the spatial public goods game model. Specifically, the behavior of conditional exclusion depends on the number of defectors in the group and can be adjusted by a tolerance parameter. Only if the number of defectors in the group exceeds the tolerance threshold, conditional exclusion can be triggered to exclude defectors. We explore the effects of parameters such as tolerance, exclusion cost, and probability of exclusion success on the evolution of cooperation. Simulation results confirmed that conditional exclusion can greatly reduce the threshold values of the synergy factor above which cooperation can emerge. Especially, when the tolerance is low, very small synergy factors can promote the population to achieve a high level of cooperation. Moreover, even if the probability of exclusion success is low, or the unit exclusion cost is relatively high, conditional exclusion is effective in promoting cooperation. These results allow us to better understand the role of exclusion strategies in the emergence of cooperation.

The public goods game with shared punishment cost in well-mixed and structured populations

Both experimental and theoretical studies have shown that punishment plays an important role in promoting cooperation. Various forms of punishment are proposed to explain why costly punishment could be maintained in the population and stabilize cooperation. Here we consider an altruistic behavior that cooperators perform cooperation and punishment simultaneously and share the punishment cost. We investigate the role of punishment cost shared among cooperators in the evolution of cooperation in public goods game. We show that the punishment can promote and stabilize cooperation when the penalty imposed on defectors is large enough compared to the punishment cost incurred by cooperators in well-mixed populations. In structured populations, cooperation could emerge under lower fine threshold and coexist with defection. However, as the penalty increases, cooperation will have a larger basin of attraction in the well-mixed population than that in the structured population. Our analytical and simulated results indicate that punishment indeed can effectively promote the evolution of cooperation. We also find that population structure can promote the coexistence of cooperation and defection but not always be beneficial to 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.

Individual solutions to shared problems create a modern tragedy of the commons

Alone and together, climatic changes, population growth, and economic scarcity create shared problems that can be tackled effectively through cooperation and coordination. Perhaps because cooperation is fragile and easily breaks down, societies also provide individual solutions to shared problems, such as privatized healthcare or retirement planning. But how does the availability of individual solutions affect free-riding and the efficient creation of public goods? We confronted groups of individuals with a shared problem that could be solved either individually or collectively. Across different cost-benefit ratios of individually versus collectively solving the shared problem, individuals display a remarkable tendency toward group-independent, individual solutions. This "individualism" leads to inefficient resource allocations and coordination failure. Introducing peer punishment further results in wasteful punishment feuds between "individualists" and "collectivists." In the presence of individual solutions to shared problems, groups struggle to balance self-reliance and collective efficiency, leading to a "modern tragedy of the commons."

The rise and fall of cooperation through reputation and group polarization

Humans exhibit a remarkable capacity for cooperation among genetically unrelated individuals. Yet, human cooperation is neither universal, nor stable. Instead, cooperation is often bounded to members of particular groups, and such groups endogenously form or break apart. Cooperation networks are parochial and under constant reconfiguration. Here, we demonstrate how parochial cooperation networks endogenously emerge as a consequence of simple reputation heuristics people may use when deciding to cooperate or defect. These reputation heuristics, such as "a friend of a friend is a friend" and "the enemy of a friend is an enemy" further lead to the dynamic formation and fission of cooperative groups, accompanied by a dynamic rise and fall of cooperation among agents. The ability of humans to safeguard kin-independent cooperation through gossip and reputation may be, accordingly, closely interlinked with the formation of group-bounded cooperation networks that are under constant reconfiguration, ultimately preventing global and stable cooperation.

Bribery games on interdependent complex networks

Bribe demands present a social conflict scenario where decisions have wide-ranging economic and ethical consequences. Nevertheless, such incidents occur daily in many countries across the globe. Harassment bribery constitute a significant sub-set of such bribery incidents where a government official demands a bribe for providing a service to a citizen legally entitled to it. We employ an evolutionary game-theoretic framework to analyse the evolution of corrupt and honest strategies in structured populations characterized by an interdependent complex network. The effects of changing network topology, average number of links and asymmetry in size of the citizen and officer population on the proliferation of incidents of bribery are explored. A complex network topology is found to be beneficial for the dominance of corrupt strategies over a larger region of phase space when compared with the outcome for a regular network, for equal citizen and officer population sizes. However, the extent of the advantage depends critically on the network degree and topology. A different trend is observed when there is a difference between the citizen and officer population sizes. Under those circumstances, increasing randomness of the underlying citizen network can be beneficial to the fixation of honest officers up to a certain value of the network degree. Our analysis reveals how the interplay between network topology, connectivity and strategy update rules can affect population level outcomes in such asymmetric games.

Dispositional free riders do not free ride on punishment

Strong reciprocity explains prosocial cooperation by the presence of individuals who incur costs to help those who helped them ('strong positive reciprocity') and to punish those who wronged them ('strong negative reciprocity'). Theories of social preferences predict that in contrast to 'strong reciprocators', self-regarding people cooperate and punish only if there are sufficient future benefits. Here, we test this prediction in a two-stage design. First, participants are classified according to their disposition towards strong positive reciprocity as either dispositional conditional cooperators (DCC) or dispositional free riders (DFR). Participants then play a one-shot public goods game, either with or without punishment. As expected, DFR cooperate only when punishment is possible, whereas DCC cooperate without punishment. Surprisingly, dispositions towards strong positive reciprocity are unrelated to strong negative reciprocity: punishment by DCC and DFR is practically identical. The 'burden of cooperation' is thus carried by a larger set of individuals than previously assumed.

Changes in political party systems arising from conflict and transfer among political parties

Conflict that arises between two groups of different paradigms is an inevitable phenomenon, and a representative example of the conflict among different groups is a conflict phenomenon caused by competition among political parties. In this paper, we study the dynamical behavior of a political party system. Considering three major political parties, we investigate how political party systems can be changed by employing a mathematical model. By considering the transfer mechanism of recruitment as well as conflict of competition between political parties, we found that all parties are likely to coexist when both the competition and transfer between the parties are weak, or if either mechanism can occur at a relatively low level. Otherwise, a political party system is changed to a single-party system. In addition, we found that when a party system was changed into a single-party system, it appeared to be either bistable or multistable, and has been elucidate by linear stability analysis. Our results may provide insights to understand mechanisms how political party systems can be changed by conflict and transfer.

Strategy intervention for the evolution of fairness

The 'irrational' preference for fairness has attracted increasing attention. Although previous studies have focused on the effects of spitefulness on the evolution of fairness, they did not consider non-monotonic rejections shown in behavioral experiments. In this paper, we introduce a non-monotonic rejection in an evolutionary model of the Ultimatum Game. We propose strategy intervention to study the evolution of fairness in general structured populations. By sequentially adding five strategies into the competition between a fair strategy and a selfish strategy, we arrive at the following conclusions. First, the evolution of fairness is inhibited by altruism, but it is promoted by spitefulness. Second, the non-monotonic rejection helps fairness overcome selfishness. Particularly for group-structured populations, we analytically investigate how fairness, selfishness, altruism, and spitefulness are affected by population size, mutation, and migration in the competition among seven strategies. Our results may provide important insights into understanding the evolutionary origin of fairness.

Why Hate the Good Guy? Antisocial Punishment of High Cooperators Is Greater When People Compete To Be Chosen

When choosing social partners, people prefer good cooperators (all else being equal). Given this preference, people wishing to be chosen can either increase their own cooperation to become more desirable or suppress others’ cooperation to make them less desirable. Previous research shows that very cooperative people sometimes get punished (“antisocial punishment”) or criticized (“do-gooder derogation”) in many cultures. Here, we used a public-goods game with punishment to test whether antisocial punishment is used as a means of competing to be chosen by suppressing others’ cooperation. As predicted, there was more antisocial punishment when participants were competing to be chosen for a subsequent cooperative task (a trust game) than without a subsequent task. This difference in antisocial punishment cannot be explained by differences in contributions, moralistic punishment, or confusion. This suggests that antisocial punishment is a social strategy that low cooperators use to avoid looking bad when high cooperators escalate cooperation.

Conditional punishment is a double-edged sword in promoting cooperation

Punishment is widely recognized as an effective approach for averting from exploitation by free-riders in human society. However, punishment is costly, and thus rational individuals are unwilling to take the punishing action, resulting in the second-order free-rider problem. Recent experimental study evidences that individuals prefer conditional punishment, and their punishing decision depends on other members' punishing decisions. In this work, we thus propose a theoretical model for conditional punishment and investigate how such conditional punishment influences cooperation in the public goods game. Considering conditional punishers only take the punishing action when the number of unconditional punishers exceeds a threshold number, we demonstrate that such conditional punishment induces the effect of a double-edged sword on the evolution of cooperation both in well-mixed and structured populations. Specifically, when it is relatively easy for conditional punishers to engage in the punishment activity corresponding to a low threshold value, cooperation can be promoted in comparison with the case without conditional punishment. Whereas when it is relatively difficult for conditional punishers to engage in the punishment activity corresponding to a high threshold value, cooperation is inhibited in comparison with the case without conditional punishment. Moreover, we verify that such double-edged sword effect exists in a wide range of model parameters and can be still observed in other different punishment regimes.

Stochastic evolutionary voluntary public goods game with punishment in a Quasi-birth-and-death process

Traditional replication dynamic model and the corresponding concept of evolutionary stable strategy (ESS) only takes into account whether the system can return to the equilibrium after being subjected to a small disturbance. In the real world, due to continuous noise, the ESS of the system may not be stochastically stable. In this paper, a model of voluntary public goods game with punishment is studied in a stochastic situation. Unlike the existing model, we describe the evolutionary process of strategies in the population as a generalized quasi-birth-and-death process. And we investigate the stochastic stable equilibrium (SSE) instead. By numerical experiments, we get all possible SSEs of the system for any combination of parameters, and investigate the influence of parameters on the probabilities of the system to select different equilibriums. It is found that in the stochastic situation, the introduction of the punishment and non-participation strategies can change the evolutionary dynamics of the system and equilibrium of the game. There is a large range of parameters that the system selects the cooperative states as its SSE with a high probability. This result provides us an insight and control method for the evolution of cooperation in the public goods game in stochastic situations.

Behavioural Differences and Neural Substrates of Altruistic and Spiteful Punishment

Altruistic punishment following social norm violations promotes human cooperation. However, experimental evidence indicates that some forms of punishment are spiteful rather than altruistic. Using two types of punishment games and seven non-strategic games, we identified strong behavioural differences between altruistic and spiteful punishers. Altruistic punishers who rejected unfair offers in the ultimatum game and punished norm violators in the third-party punishment game behaved pro-socially in various non-strategic games. Spiteful punishers who rejected unfair offers in the ultimatum game but did not punish norm violators in the third-party punishment game behaved selfishly in non-strategic games. In addition, the left caudate nucleus was larger in spiteful punishers than in altruistic punishers. These findings are in contrast to the previous assumption that altruistic punishers derive pleasure from enforcement of fairness norms, and suggest that spiteful punishers derive pleasure from seeing the target experience negative consequences.

Costly Punishment Increases Prosocial Punishment by Designated Punishers: Power and Legitimacy in Public Goods Games

A classic problem in the literature on authority is that those with the power to enforce cooperation and proper norms of conduct can also abuse or misuse their power. The present research tested the argument that concerns about legitimacy can help regulate the use of power to punish by invoking a sense of what is morally right or socially proper for power-holders. We tested this idea in a laboratory experiment using public goods games in which one person in each group was selected to be a “designated punisher” who could give out material punishment that was either costly or costless to the punisher. Results show that costly punishment is perceived as more legitimate (proper) than costless punishment and that designated punishers engaged in more proper (“prosocial”) punishment and less abusive (“antisocial”) punishment when punishment was costly. These results highlight the importance of legitimacy in both motivating and regulating the enforcement of cooperation.