The take-it-or-leave-it option allows small penalties to overcome social dilemmas

Discipline and punishment in panoptical public goods games

In Public Goods Games (PGG), the temptation to free-ride on others' contributions poses a significant threat to the sustainability of cooperative societies. Therefore, societies strive to mitigate this through incentive systems, employing rewards and punishments to foster cooperative behavior. Thus, peer punishment, in which cooperators sanction defectors, as well as pool punishment, where a centralized punishment institution executes the punishment, is deeply analyzed in previous works. Although the literature indicates that these methods may enhance cooperation on social dilemmas under particular contexts, there are still open questions, for instance, the structural connection between graduated punishment and the monitoring of public goods games. Our investigation proposes a compulsory PGG framework under Panoptical surveillance. Inspired by Foucault's theories on disciplinary mechanisms and biopower, we present a novel mathematical model that scrutinizes the balance between the severity and scope of punishment to catalyze cooperative behavior. By integrating perspectives from evolutionary game theory and Foucault's theories of power and discipline, this research uncovers the theoretical foundations of mathematical frameworks involved in punishment and discipline structures. We show that well-calibrated punishment and discipline schemes, leveraging the panoptical effect for universal oversight, can effectively mitigate the free-rider dilemma, fostering enhanced cooperation. This interdisciplinary approach not only elucidates the dynamics of cooperation in societal constructs but also underscores the importance of integrating diverse methodologies to address the complexities of fostering cooperative evolution.

Cost optimisation of hybrid institutional incentives for promoting cooperation in finite populations

In this paper, we rigorously study the problem of cost optimisation of hybrid (mixed) institutional incentives, which are a plan of actions involving the use of reward and punishment by an external decision-maker, for maximising the level (or guaranteeing at least a certain level) of cooperative behaviour in a well-mixed, finite population of self-regarding individuals who interact via cooperation dilemmas (Donation Game or Public Goods Game). We show that a mixed incentive scheme can offer a more cost-efficient approach for providing incentives while ensuring the same level or standard of cooperation in the long-run. We establish the asymptotic behaviour (namely neutral drift, strong selection, and infinite-population limits). We prove the existence of a phase transition, obtaining the critical threshold of the strength of selection at which the monotonicity of the cost function changes and providing an algorithm for finding the optimal value of the individual incentive cost. Our analytical results are illustrated with numerical investigations. Overall, our analysis provides novel theoretical insights into the design of cost-efficient institutional incentive mechanisms for promoting the evolution of cooperation in stochastic systems.

Managing ecological thresholds of a risky commons

Common resources are often overexploited and appear subject to critical transitions from one stable state to another antagonistic state. Many times resulting in tragedy of the commons (TOC)-exploitation of shared resources for personal gain/payoffs, leading to worse outcomes or extinction. An adequate response would be strategic interaction, such as inspection and punishment by institutions to avoid TOC. This strategic interaction is often coupled with dynamically changing common resources. However, effect of strategic interaction in complex, coupled socio-ecological systems is less studied. Here, we develop replicator equations using evolving games in which strategy and common resources co-evolve. We consider the shared commons as fish dynamics governed by the intrinsic growth rate, predation and harvesting. The joint dynamics exhibit an oscillatory TOC, revealing that institutions need to pay special attention to intrinsic growth rate and nonlinear interaction. Our research shows that the co-evolving system exhibits a broader range of dynamics when predation is present compared to the disengaged fishery system. We conclude that the usefulness, chances and challenges of modelling co-evolutionary games to create sustainable systems merit further research.

Cooperation and coordination in heterogeneous populations

One landmark application of evolutionary game theory is the study of social dilemmas. This literature explores why people cooperate even when there are strong incentives to defect. Much of this literature, however, assumes that interactions are symmetric. Individuals are assumed to have the same strategic options and the same potential pay-offs. Yet many interesting questions arise once individuals are allowed to differ. Here, we study asymmetry in simple coordination games. In our set-up, human participants need to decide how much of their endowment to contribute to a public good. If a group's collective contribution reaches a pre-defined threshold, all group members receive a reward. To account for possible asymmetries, individuals either differ in their endowments or their productivities. According to a theoretical equilibrium analysis, such games tend to have many possible solutions. In equilibrium, group members may contribute the same amount, different amounts or nothing at all. According to our behavioural experiment, however, humans favour the equilibrium in which everyone contributes the same proportion of their endowment. We use these experimental results to highlight the non-trivial effects of inequality on cooperation, and we discuss to which extent models of evolutionary game theory can account for these effects. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Optimization of institutional incentives for cooperation in structured populations

The application of incentives, such as reward and punishment, is a frequently applied way for promoting cooperation among interacting individuals in structured populations. However, how to properly use the incentives is still a challenging problem for incentive-providing institutions. In particular, since the implementation of incentive is costly, to explore the optimal incentive protocol, which ensures the desired collective goal at a minimal cost, is worthy of study. In this work, we consider the positive and negative incentives for a structured population of individuals whose conflicting interactions are characterized by a Prisoner's Dilemma game. We establish an index function for quantifying the cumulative cost during the process of incentive implementation, and theoretically derive the optimal positive and negative incentive protocols for cooperation on regular networks. We find that both types of optimal incentive protocols are identical and time-invariant. Moreover, we compare the optimal rewarding and punishing schemes concerning implementation cost and provide a rigorous basis for the usage of incentives in the game-theoretical framework. We further perform computer simulations to support our theoretical results and explore their robustness for different types of population structures, including regular, random, small-world and scale-free networks.

Network Characteristic Control of Social Dilemmas in a Public Good Game: Numerical Simulation of Agent-Based Nonlinear Dynamics

This paper proposes a possible mechanism for obtaining sizeable behavioral structures by simulating a network–agent dynamic on an evolutionary public good game with available social .learning. The model considers a population with a fixed number of players. In each round, the chosen players may contribute part of their value to a common pool. Then, each player may imitate the strategy of another player based on relative payoffs (whoever has the lower payoff adopts the strategy of the other player) and change his or her strategy using different exploratory variables. Relative payoffs are subject to incentives, including participation costs, but may also be subject to mutation, whose rate is sensitized by the network characteristics (social ties). The process discussed in this report is interesting and relevant across a broad range of disciplines that use game theory, including cultural evolutionary dynamics.

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.

Joint effects of voluntary participation and group selection on the evolution of altruistic punishment

It is puzzling how altruistic punishment of defectors can evolve in large groups of nonrelatives, since punishers should voluntarily bear individual costs of punishing to benefit those who do not pay the costs. Although two distinct mechanisms have been proposed to explain the puzzle, namely voluntary participation and group-level competition and selection, insights into their joint effects have been less clear. Here we investigated what could be combined effects of these two mechanisms on the evolution of altruistic punishment and how these effects can vary with nonparticipants’ individual payoff and group size. We modelled altruistic punishers as those who contribute to a public good and impose a fine on each defector, i.e., they are neither pure punishers nor excluders. Our simulation results show that voluntary participation has negative effects on the evolution of cooperation in small groups regardless of nonparticipants’ payoffs, while in large groups it has positive effects within only a limited range of nonparticipants’ payoff. We discuss that such asymmetric effects could be explained by evolutionary forces emerging from voluntary participation. Lastly, we suggest that insights from social science disciplines studying the exit option could enrich voluntary participation models.

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.

Cost efficiency of institutional incentives for promoting cooperation in finite populations

Institutions can provide incentives to enhance cooperation in a population where this behaviour is infrequent. This process is costly, and it is thus important to optimize the overall spending. This problem can be mathematically formulated as a multi-objective optimization problem where one wishes to minimize the cost of providing incentives while ensuring a minimum level of cooperation, sustained over time. Prior works that consider this question usually omit the stochastic effects that drive population dynamics. In this paper, we provide a rigorous analysis of this optimization problem, in a finite population and stochastic setting, studying both pairwise and multi-player cooperation dilemmas. We prove the regularity of the cost functions for providing incentives over time, characterize their asymptotic limits (infinite population size, weak selection and large selection) and show exactly when reward or punishment is more cost efficient. We show that these cost functions exhibit a phase transition phenomenon when the intensity of selection varies. By determining the critical threshold of this phase transition, we provide exact calculations for the optimal cost of the incentive, for any given intensity of selection. Numerical simulations are also provided to demonstrate analytical observations. Overall, our analysis provides for the first time a selection-dependent calculation of the optimal cost of institutional incentives (for both reward and punishment) that guarantees a minimum level of cooperation over time. It is of crucial importance for real-world applications of institutional incentives since the intensity of selection is often found to be non-extreme and specific for a given population.

Combination of institutional incentives for cooperative governance of risky commons

Finding appropriate incentives to enforce collaborative efforts for governing the commons in risky situations is a long-lasting challenge. Previous works have demonstrated that both punishing free-riders and rewarding cooperators could be potential tools to reach this goal. Despite weak theoretical foundations, policy makers frequently impose a punishment-reward combination. Here, we consider the emergence of positive and negative incentives and analyze their simultaneous impact on sustaining risky commons. Importantly, we consider institutions with fixed and flexible incentives. We find that a local sanctioning scheme with pure reward is the optimal incentive strategy. It can drive the entire population toward a highly cooperative state in a broad range of parameters, independently of the type of institutions. We show that our finding is also valid for flexible incentives in the global sanctioning scheme, although the local arrangement works more effectively.

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Pure reward in a local scheme is more effective both for fixed and flexible incentives

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It can drive the entire population toward a highly cooperative state

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Increasing the efficiency of the institution can induce the success of pure reward

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A local scheme promotes group success more effectively than a global scheme

Reward and punishment in a team contest

A team contest entails both public good characteristics within the teams as well as a contest across teams. In an experimental study, we analyse behaviour in such a team contest when allowing to punish or to reward other team members. Moreover, we compare two types of contest environment: One in which two teams compete for a prize and another one in which we switch off the between-group element of the contest. We find that reward giving, as opposed to punishing, induces higher contributions to the team contest. Furthermore, expenditures on rewarding other co-players are significantly higher than those for punishing.

Governance of risky public goods under graduated punishment

Ensuring global cooperation often poses governance problems shadowed by the tragedy of the commons, as wrong-doers enjoy the benefits set up by right-doers at no cost. Institutional punishment of wrong-doers is well-known to curtail their impetus as free-riders. However, institutions often have limited scope in imposing sanctions, more so when these are strict and potentially viewed as disproportionate. Inspired by the design principles proposed by the late Nobel Prize Elinor Ostrom, here we study the evolution and impact of a new form of institutional sanctioning, where punishment is graduated, growing with the incidence of free-riding. We develop an analytical model capable of identifying the conditions under which this design principle is conducive to the self-organization of stable institutions and cooperation. We employ evolutionary game theory in finite populations and non-linear public goods dilemmas in the presence of risk of global losses whose solution requires the self-organization of decision makers into an overall cooperative state. We show that graduated punishment is more effective in promoting widespread cooperation than conventional forms of punishment studied to date, being also less severe and thus, presumably, easier to implement. This effect is enhanced whenever the costs of its implementation are positively correlated with the severity of punishment. We frame our model within the context of the global reduction of carbon emissions, but the results are shown to be general enough to be applicable to other collective action problems, shedding further light into the origins of Human institutions.

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.

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.

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.

Which is the ideal sanction for cooperation? An experimental study on different types of third-party sanctions

Cooperation is the crux of many social problems, thus third‐party sanction, as one of the most important ways to promote cooperation, is worth studying. The present study compared the effects of third‐party punishment alone, third‐party reward alone, and the combination of third‐party reward and third‐party punishment on cooperation in the context of a public goods experiment. In addition, we explored the characteristics of third‐party sanctioning behaviors. A total of 280 students participated in the present study. The results showed that the operation of third‐party sanctions did raise the level of cooperation and changed the discrete trend of cooperation—specifically, the differences between the cooperation level of every group member and the average level of the whole group. Furthermore, when third‐party rewards and third‐party punishments were used simultaneously in the public goods game (PGG), the level of cooperation was greatly enhanced, which meant that in the context of the third party, when punishment opportunities and reward opportunities coexist, they may have a “compensatory effect.” In terms of the characteristics of sanctioning behaviors, the frequency of third‐party sanctions did not differ significantly under different conditions (third‐party punishment alone, third‐party reward alone, and a combination of third‐party reward and third‐party punishment), and neither did expenditures on third‐party sanctions, but the strategies that third parties used changed under different conditions, thus their effects on other group members’ cooperative behavior varied under different conditions. The present study provides a comprehensive picture of how third parties behave in different conditions of third‐party sanctions and how these sanctions exert influence on cooperation. Understanding these mechanisms can help us build more effective institutions.

Cost-effective external interference for promoting the evolution of cooperation

The problem of promoting the evolution of cooperative behaviour within populations of self-regarding individuals has been intensively investigated across diverse fields of behavioural, social and computational sciences. In most studies, cooperation is assumed to emerge from the combined actions of participating individuals within the populations, without taking into account the possibility of external interference and how it can be performed in a cost-efficient way. Here, we bridge this gap by studying a cost-efficient interference model based on evolutionary game theory, where an exogenous decision-maker aims to ensure high levels of cooperation from a population of individuals playing the one-shot Prisoner’s Dilemma, at a minimal cost. We derive analytical conditions for which an interference scheme or strategy can guarantee a given level of cooperation while at the same time minimising the total cost of investment (for rewarding cooperative behaviours), and show that the results are highly sensitive to the intensity of selection by interference. Interestingly, we show that a simple class of interference that makes investment decisions based on the population composition can lead to significantly more cost-efficient outcomes than standard institutional incentive strategies, especially in the case of weak selection.

Endogenous rewards promote cooperation

An important research area in the social and biological sciences is how endogenous sanctions can promote cooperation in social dilemma situations, particularly in a budget-balanced (no need for external financing) manner. Punishment has had some success in experimental studies, but has serious shortcomings: It is socially wasteful materially and also tends to induce poor social relations. Reward avoids those issues and reinforces the social fabric. Our mechanism achieves high contributions in a public goods game (PGG) with peer reward in a budget-balanced tax-funding environment; notably, our environment also reverses the downward trend of the standard PGG. This research advances the field in a direction that will be important for practical policy applications, opening the door for further interesting and socially beneficial research.

Sustaining cooperation in social dilemmas is a fundamental objective in the social and biological sciences. Although providing a punishment option to community members in the public goods game (PGG) has been shown to effectively promote cooperation, this has some serious disadvantages; these include destruction of a society’s physical resources as well as its overall social capital. A more efficient approach may be to instead employ a reward mechanism. We propose an endogenous reward mechanism that taxes the gross income of each round’s PGG play and assigns the amount to a fund; each player then decides how to distribute his or her share of the fund as rewards to other members of the community. Our mechanism successfully reverses the decay trend and achieves a high level of contribution with budget-balanced rewards that require no external funding, an important condition for practical implementation. Simulations based on type-specific estimations indicate that the payoff-based conditional cooperation model explains the observed treatment effects well.

Punishment and inspection for governing the commons in a feedback-evolving game

Utilizing common resources is always a dilemma for community members. While cooperator players restrain themselves and consider the proper state of resources, defectors demand more than their supposed share for a higher payoff. To avoid the tragedy of the common state, punishing the latter group seems to be an adequate reaction. This conclusion, however, is less straightforward when we acknowledge the fact that resources are finite and even a renewable resource has limited growing capacity. To clarify the possible consequences, we consider a coevolutionary model where beside the payoff-driven competition of cooperator and defector players the level of a renewable resource depends sensitively on the fraction of cooperators and the total consumption of all players. The applied feedback-evolving game reveals that beside a delicately adjusted punishment it is also fundamental that cooperators should pay special attention to the growing capacity of renewable resources. Otherwise, even the usage of tough punishment cannot save the community from an undesired end.

Our proposed model considers not only the fundamental dilemma of individual and collective benefits but also focuses on their impacts on the environmental state. In general, there is a strong interdependence between individual actions and the actual shape of environment that can be described by means of a co-evolutionary model. Such approach recognizes the fact that even if our common-pool resources are partly renewable, they have limited growth capacities hence a depleted environment is unable to recover and reach a sustainable level again. This scenario would have a dramatic consequence on our whole society, therefore we should avoid it by punishing those who are not exercising restrain. We provide analytical and numerical evidences which highlight that punishment alone may not necessarily be a powerful tool to maintain a healthy shape of environment for the benefit of future generations. Cooperator actors, who are believed to take care of present state of our environment, should also consider carefully the growth capacity of renewable resources.

Evolution of cooperation in a hierarchical society with corruption control

Punishment is widely recognized as a potential promoter in sustaining or even enhancing public cooperation, but it meanwhile induces the problem of second-order free-riders. Particularly, recent evidence shows that costly punishment can be maintained if punishers may engage in corruption. However, how to reduce or eliminate incidents of corruption has been the enduring conundrum in human society. As power asymmetries are associated with hierarchies, we investigate how costly punishment affects the evolution of cooperation in the cases without and with corruption control. In the absence of corruption control, altruistic punishers are incapable of punishing corrupt punishers. Corrupt punishment maintains civilian cooperation but undermines the evolution of altruistic punishment. Otherwise, altruistic punishers can enforce symmetrical or asymmetrical punishment on both corrupt punishers and civilian defectors. In this case, both civilian cooperation and altruistic punishment can be promoted. And as an instrument of corruption control, the policy of asymmetrical punishment is more effective in fostering public cooperation and improving social welfare than symmetrical punishment. Moreover, no matter whether corruption control is considered or not, spiteful corruption that non-cooperative punishers penalize defectors is a more effective form for enhancing cooperation compared with bribery. Our work may thus offer an insight into the effects of corruption on public cooperation and the policy of anti-corruption.

The Institutional Approach for Modeling the Evolution of Human Societies

Artificial life is concerned with understanding the dynamics of human societies. A defining feature of any society is its institutions. However, defining exactly what an institution is has proven difficult, with authors often talking past each other. This article presents a dynamic model of institutions, which views them as political game forms that generate the rules of a group's economic interactions. Unlike most prior work, the framework presented here allows for the construction of explicit models of the evolution of institutional rules. It takes account of the fact that group members are likely to try to create rules that benefit themselves. Following from this, it allows us to determine the conditions under which self-interested individuals will create institutional rules that support cooperation-for example, that prevent a tragedy of the commons. The article finishes with an example of how a model of the evolution of institutional rewards and punishments for promoting cooperation can be created. It is intended that this framework will allow artificial life researchers to examine how human groups can themselves create conditions for cooperation. This will help provide a better understanding of historical human social evolution, and facilitate the resolution of pressing societal social dilemmas.

Asymmetric public goods game cooperation through pest control

Cooperation in a public goods game has been studied extensively to find the conditions for sustaining the commons, yet the effect of asymmetry between agents has been explored very little. Here we study a game theoretic model of cooperation for pest control among farmers. In our simple model, each farmer has a paddy of the same size arranged adjacently on a line. A pest outbreak occurs at an abandoned paddy at one end of the line, directly threatening the frontier farmer adjacent to it. Each farmer pays a cost of his or her choice to an agricultural collective, and the total sum held by the collective is used for pest control, with success probability increasing with the sum. Because the farmers' incentives depend on their distance from the pest outbreak, our model is an asymmetric public goods game. We derive each farmer's cost strategy at the Nash equilibrium. We find that asymmetry among farmers leads to a few unexpected outcomes. The individual costs at the equilibrium do not necessarily increase with how much the future is valued but rather show threshold behavior. Moreover, an increase in the number of farmers can sometimes paradoxically undermine pest prevention. A comparison with a symmetric public goods game model reveals that the farmer at the greatest risk pays a disproportionate amount of cost in the asymmetric game, making the use of agricultural lands less sustainable.

Voluntary vaccination dilemma with evolving psychological perceptions

Voluntary vaccination is a universal control protocol for infectious diseases. Yet there exists a social dilemma between individual benefits and public health: non-vaccinators free ride via the herd immunity from adequate vaccinators who bear vaccination cost. This is due to the interplay between disease prevalence and individual vaccinating behavior. To complicate matters further, individual vaccinating behavior depends on the perceived vaccination cost rather than the actual one. The perception of vaccination cost is an individual trait, which varies from person to person, and evolves in response to the disease prevalence and vaccination coverage. To explore how evolving perception shapes individual vaccinating behavior and thus the vaccination dynamics, we provide a model combining epidemic dynamics with evolutionary game theory which captures the voluntary vaccination dilemma. In particular, individuals adjust their perception based on the inertia effect in psychology and then update their vaccinating behavior through imitating the behavior of a more successful peer. We find that i) vaccination is acceptable when the expected vaccination cost considering perception and actual vaccination cost is less than the maximum of the expected non-vaccination cost; ii) the evolution of perception is a "double-edged sword" for vaccination dynamics: it can improve vaccination coverage when most individuals perceive exaggerated vaccination cost, and it inhibits vaccination coverage in the other cases.

Individual wealth-based selection supports cooperation in spatial public goods games

In a social dilemma game group members are allowed to decide if they contribute to the joint venture or not. As a consequence, defectors, who do not invest but only enjoy the mutual benefit, prevail and the system evolves onto the tragedy of the common state. This unfortunate scenario can be avoided if participation is not obligatory but only happens with a given probability. But what if we also consider a player’s individual wealth when to decide about participation? To address this issue we propose a model in which the probabilistic participation in the public goods game is combined with a conditional investment mode that is based on individual wealth: if a player’s wealth exceeds a threshold value then it is qualified and can participate in the joint venture. Otherwise, the participation is forbidden in the investment interactions. We show that if only probabilistic participation is considered, spatially structured populations cannot support cooperation better than well-mixed populations where full defection state can also be avoided for small participation probabilities. By adding the wealth-based criterion of participation, however, structured populations are capable to augment network reciprocity relevantly and allow cooperator strategy to dominate in a broader parameter interval.

The dynamics of human behavior in the public goods game with institutional incentives

The empirical research on the public goods game (PGG) indicates that both institutional rewards and institutional punishment can curb free-riding and that the punishment effect is stronger than the reward effect. Self-regarding models that are based on Nash equilibrium (NE) strategies or evolutionary game dynamics correctly predict which incentives are best at promoting cooperation, but individuals do not play these rational strategies overall. The goal of our study is to investigate the dynamics of human decision making in the repeated PGG with institutional incentives. We consider that an individual's contribution is affected by four factors, which are self-interest, the behavior of others, the reaction to rewards, and the reaction to punishment. We find that people on average do not react to rewards and punishment, and that self-interest and the behavior of others sufficiently explain the dynamics of human behavior. Further analysis suggests that institutional incentives promote cooperation by affecting the self-regarding preference and that the other-regarding preference seems to be independent of incentive schemes. Because individuals do not change their behavioral patterns even if they were not rewarded or punished, the mere potential to punish defectors and reward cooperators can lead to considerable increases in the level of cooperation.

Eco-evolutionary dynamics of social dilemmas

Social dilemmas are an integral part of social interactions. Cooperative actions, ranging from secreting extra-cellular products in microbial populations to donating blood in humans, are costly to the actor and hence create an incentive to shirk and avoid the costs. Nevertheless, cooperation is ubiquitous in nature. Both costs and benefits often depend non-linearly on the number and types of individuals involved-as captured by idioms such as 'too many cooks spoil the broth' where additional contributions are discounted, or 'two heads are better than one' where cooperators synergistically enhance the group benefit. Interaction group sizes may depend on the size of the population and hence on ecological processes. This results in feedback mechanisms between ecological and evolutionary processes, which jointly affect and determine the evolutionary trajectory. Only recently combined eco-evolutionary processes became experimentally tractable in microbial social dilemmas. Here we analyse the evolutionary dynamics of non-linear social dilemmas in settings where the population fluctuates in size and the environment changes over time. In particular, cooperation is often supported and maintained at high densities through ecological fluctuations. Moreover, we find that the combination of the two processes routinely reveals highly complex dynamics, which suggests common occurrence in nature.

When is bigger better? The effects of group size on the evolution of helping behaviours

Understanding the evolution of sociality in humans and other species requires understanding how selection on social behaviour varies with group size. However, the effects of group size are frequently obscured in the theoretical literature, which often makes assumptions that are at odds with empirical findings. In particular, mechanisms are suggested as supporting large-scale cooperation when they would in fact rapidly become ineffective with increasing group size. Here we review the literature on the evolution of helping behaviours (cooperation and altruism), and frame it using a simple synthetic model that allows us to delineate how the three main components of the selection pressure on helping must vary with increasing group size. The first component is the marginal benefit of helping to group members, which determines both direct fitness benefits to the actor and indirect fitness benefits to recipients. While this is often assumed to be independent of group size, marginal benefits are in practice likely to be maximal at intermediate group sizes for many types of collective action problems, and will eventually become very small in large groups due to the law of decreasing marginal returns. The second component is the response of social partners on the past play of an actor, which underlies conditional behaviour under repeated social interactions. We argue that under realistic conditions on the transmission of information in a population, this response on past play decreases rapidly with increasing group size so that reciprocity alone (whether direct, indirect, or generalised) cannot sustain cooperation in very large groups. The final component is the relatedness between actor and recipient, which, according to the rules of inheritance, again decreases rapidly with increasing group size. These results explain why helping behaviours in very large social groups are limited to cases where the number of reproducing individuals is small, as in social insects, or where there are social institutions that can promote (possibly through sanctioning) large-scale cooperation, as in human societies. Finally, we discuss how individually devised institutions can foster the transition from small-scale to large-scale cooperative groups in human evolution.

Promote or hinder? The role of punishment in the emergence of cooperation

Investigation of anti-social punishment has shaken the positive role of punishment in the evolution of cooperation. However, punishment is ubiquitous in nature, and the centralized, apposed to decentralized, punishment is more favored by certain modern societies in particular. To explore the underlying principle of such phenomenon, we study the evolution of cooperation in the context of pro- and anti-social punishments subject to two distinct patterns: costly centralized and decentralized punishments. The results suggest that the pattern of punishment has a great effect on the role of punishment in the evolution of cooperation. In the absence of anti-social punishment, the costly centralized punishment is more effective in promoting the emergence of cooperation. Anti-social punishment can subvert the positive role of punishment when anti- and pro-social punishments are in the same pattern. However, driven by centralized pro-social punishment, cooperation can be more advantageous than defection even in the presence of decentralized anti-social punishment.

Evolution of public cooperation in a monitored society with implicated punishment and within-group enforcement

Monitoring with implicated punishment is common in human societies to avert freeriding on common goods. But is it effective in promoting public cooperation? We show that the introduction of monitoring and implicated punishment is indeed effective, as it transforms the public goods game to a coordination game, thus rendering cooperation viable in infinite and finite well-mixed populations. We also show that the addition of within-group enforcement further promotes the evolution of public cooperation. However, although the group size in this context has nonlinear effects on collective action, an intermediate group size is least conductive to cooperative behaviour. This contradicts recent field observations, where an intermediate group size was declared optimal with the conjecture that group-size effects and within-group enforcement are responsible. Our theoretical research thus clarifies key aspects of monitoring with implicated punishment in human societies, and additionally, it reveals fundamental group-size effects that facilitate prosocial collective action.

First carrot, then stick: how the adaptive hybridization of incentives promotes cooperation

Social institutions often use rewards and penalties to promote cooperation. Providing incentives tends to be costly, so it is important to find effective and efficient policies for the combined use of rewards and penalties. Most studies of cooperation, however, have addressed rewarding and punishing in isolation and have focused on peer-to-peer sanctioning as opposed to institutional sanctioning. Here, we demonstrate that an institutional sanctioning policy we call ‘first carrot, then stick’ is unexpectedly successful in promoting cooperation. The policy switches the incentive from rewarding to punishing when the frequency of cooperators exceeds a threshold. We find that this policy establishes and recovers full cooperation at lower cost and under a wider range of conditions than either rewards or penalties alone, in both well-mixed and spatial populations. In particular, the spatial dynamics of cooperation make it evident how punishment acts as a ‘booster stage’ that capitalizes on and amplifies the pro-social effects of rewarding. Together, our results show that the adaptive hybridization of incentives offers the ‘best of both worlds’ by combining the effectiveness of rewarding in establishing cooperation with the effectiveness of punishing in recovering it, thereby providing a surprisingly inexpensive and widely applicable method of promoting cooperation.

The evolution of anti-social rewarding and its countermeasures in public goods games

Cooperation in joint enterprises can easily break down when self-interests are in conflict with collective benefits, causing a tragedy of the commons. In such social dilemmas, the possibility for contributors to invest in a common pool-rewards fund, which will be shared exclusively among contributors, can be powerful for averting the tragedy, as long as the second-order dilemma (i.e. withdrawing contribution to reward funds) can be overcome (e.g. with second-order sanctions). However, the present paper reveals the vulnerability of such pool-rewarding mechanisms to the presence of reward funds raised by defectors and shared among them (i.e. anti-social rewarding), as it causes a cooperation breakdown, even when second-order sanctions are possible. I demonstrate that escaping this social trap requires the additional condition that coalitions of defectors fare poorly compared with pro-socials, with either (i) better rewarding abilities for the latter or (ii) reward funds that are contingent upon the public good produced beforehand, allowing groups of contributors to invest more in reward funds than groups of defectors. These results suggest that the establishment of cooperation through a collective positive incentive mechanism is highly vulnerable to anti-social rewarding and requires additional countermeasures to act in combination with second-order sanctions.

Competition and cooperation among different punishing strategies in the spatial public goods game

Inspired by the fact that people have diverse propensities to punish wrongdoers, we study a spatial public goods game with defectors and different types of punishing cooperators. During the game, cooperators punish defectors with class-specific probabilities and subsequently share the associated costs of sanctioning. We show that in the presence of different punishing cooperators the highest level of public cooperation is always attainable through a selection mechanism. Interestingly, the selection does not necessarily favor the evolution of punishers who would be able to prevail on their own against the defectors, nor does it always hinder the evolution of punishers who would be unable to prevail on their own. Instead, the evolutionary success of punishing strategies depends sensitively on their invasion velocities, which in turn reveals fascinating examples of both competition and cooperation among them. Furthermore, we show that under favorable conditions, when punishment is not strictly necessary for the maintenance of public cooperation, the less aggressive, mild form of sanctioning is the sole victor of the selection process. Our work reveals that natural strategy selection cannot only promote, but sometimes also hinders competition among prosocial strategies.

Evolutionary performance of zero-determinant strategies in multiplayer games

Repetition is one of the key mechanisms to maintain cooperation. In long-term relationships, in which individuals can react to their peers׳ past actions, evolution can promote cooperative strategies that would not be stable in one-shot encounters. The iterated prisoner׳s dilemma illustrates the power of repetition. Many of the key strategies for this game, such as ALLD, ALLC, Tit-for-Tat, or generous Tit-for-Tat, share a common property: players using these strategies enforce a linear relationship between their own payoff and their co-player׳s payoff. Such strategies have been termed zero-determinant (ZD). Recently, it was shown that ZD strategies also exist for multiplayer social dilemmas, and here we explore their evolutionary performance. For small group sizes, ZD strategies play a similar role as for the repeated prisoner׳s dilemma: extortionate ZD strategies are critical for the emergence of cooperation, whereas generous ZD strategies are important to maintain cooperation. In large groups, however, generous strategies tend to become unstable and selfish behaviors gain the upper hand. Our results suggest that repeated interactions alone are not sufficient to maintain large-scale cooperation. Instead, large groups require further mechanisms to sustain cooperation, such as the formation of alliances or institutions, or additional pairwise interactions between group members.

The Effect of Incentives and Meta-incentives on the Evolution of Cooperation

Although positive incentives for cooperators and/or negative incentives for free-riders in social dilemmas play an important role in maintaining cooperation, there is still the outstanding issue of who should pay the cost of incentives. The second-order free-rider problem, in which players who do not provide the incentives dominate in a game, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players’ incentives. The critical assumption of our model is that players who tend to provide incentives to other players for their cooperative or non-cooperative behavior also tend to provide incentives to their incentive behaviors. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We find that the second-order free-rider problem is completely resolved without any third-order or higher (meta) incentive under the assumption. To do so, a second-order costly incentive, which is given individually (peer-to-peer) after playing donation games, is needed. The paper concludes that (1) second-order incentives for first-order reward are necessary for cooperative regimes, (2) a system without first-order rewards cannot maintain a cooperative regime, (3) a system with first-order rewards and no incentives for rewards is the worst because it never reaches cooperation, and (4) a system with rewards for incentives is more likely to be a cooperative regime than a system with punishments for incentives when the cost-effect ratio of incentives is sufficiently large. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives.

Although social dilemmas can be resolved if punishing non-cooperators or rewarding cooperators works, such rewards and punishments, i.e., external incentives, entail certain expenses. As a result, a cooperative player who shirks his or her duty to provide an incentive to other players will emerge, and he or she will be more advantageous than an incentive-provider. In fact, the problem of excluding such cooperative incentive-non-providers, or second-order free-riders, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players’ incentives. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We show that second-order incentives for first-order reward are necessary for cooperative regimes. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives.

Discriminative host sanction together with relatedness promote the cooperation in fig/fig wasp mutualism

Sanctioning or punishing is regarded as one of the most important dynamics in the evolution of cooperation. However, it has not been empirically examined yet whether or not such enforcement selection by sanctioning or punishing and classical theories like kin or reciprocity selection are separate mechanisms contributing to the evolution of cooperation. In addition, it remains largely unclear what factors determine the intensity or effectiveness of sanction. Here, we show that in the obligate, interspecific cooperation between figs and fig wasps, the hosted figs can discriminatively sanction cheating individuals by decreasing the offspring development ratio. Concurrently, the figs can reward the cooperative pollinators with a higher offspring development ratio. This sanction intensity and effectiveness largely depend on how closely the host and symbiont are related either in terms of reciprocity exchange or genetic similarity as measured by the reciprocal of the foundress number. Our results imply that in asymmetric systems, symbionts might be forced to evolve to be cooperative or even altruistic through discriminative sanction against the noncooperative symbiont and reward to the cooperative symbiont by the host (i.e. through a game of 'carrot and stick').

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.

Decoding covert motivations of free riding and cooperation from multi-feature pattern analysis of EEG signals

Cooperation and free riding are among the most frequently observed behaviors in human social decision-making. In social interactions, the effects of strategic decision processes have been consistently reported in iterative cooperation decisions. However, the neural activity immediately after new information is presented, the time at which strategy learning potentially starts has not yet been investigated with high temporal resolution. Here, we implemented an iterative, binary public goods game that simulates cooperation/free riding behavior. We applied the multi-feature pattern analysis method by using a support vector machine and the unique combinatorial performance measure, and identified neural features from the single-trial, event-related spectral perturbation at the result-presentation of the current round that predict participants' decisions to cooperate or free ride in the subsequent round. We found that neural oscillations in centroparietal and temporal regions showed the highest predictive power through 10-fold cross-validation; these predicted the participants' next decisions, which were independent of the neural responses during their own preceding choices. We suggest that the spatial distribution and time-frequency information of the selected features represent covert motivations to free ride or cooperate in the next round and are separately processed in parallel with information regarding the preceding results.

Evolution of all-or-none strategies in repeated public goods dilemmas

Many problems of cooperation involve repeated interactions among the same groups of individuals. When collective action is at stake, groups often engage in Public Goods Games (PGG), where individuals contribute (or not) to a common pool, subsequently sharing the resources. Such scenarios of repeated group interactions materialize situations in which direct reciprocation to groups may be at work. Here we study direct group reciprocity considering the complete set of reactive strategies, where individuals behave conditionally on what they observed in the previous round. We study both analytically and by computer simulations the evolutionary dynamics encompassing this extensive strategy space, witnessing the emergence of a surprisingly simple strategy that we call All-Or-None (AoN). AoN consists in cooperating only after a round of unanimous group behavior (cooperation or defection), and proves robust in the presence of errors, thus fostering cooperation in a wide range of group sizes. The principles encapsulated in this strategy share a level of complexity reminiscent of that found already in 2-person games under direct and indirect reciprocity, reducing, in fact, to the well-known Win-Stay-Lose-Shift strategy in the limit of the repeated 2-person Prisoner's Dilemma.

The problem of cooperation has been a target of many studies, and some of the most complex dilemmas arise when we deal with groups repeatedly interacting by means of a Public Goods Game (PGG), where individuals may contribute to a common pool, subsequently sharing the resources. Here we study generalized direct group reciprocity by incorporating the complete set of reactive strategies, where action is dictated by what happened in the previous round. We compute the pervasiveness in time of each possible reactive strategy, and find a ubiquitous strategy profile that prevails throughout evolution, independently of group size and specific PGG parameters, proving also robust in the presence of errors. This strategy, that we call All-Or-None (AoN), consists in cooperating only after a round of unanimous group behavior (cooperation or defection); not only is it conceptually very simple, it also ensures that cooperation can self-sustain in a population. AoN contains core principles found, e.g., in the repeated 2-person Prisoner's Dilemma, in which case it reduces to the famous Win-Stay-Lose-Shift strategy.

Cyclic dominance in evolutionary games: a review

Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more, regardless of the particularities of the game. Here, we review recent advances on the rock-paper-scissors (RPS) and related evolutionary games, focusing, in particular, on pattern formation, the impact of mobility and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional RPS models and the application of the complex Ginzburg-Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related, for example, to dynamical effects of coevolutionary rules and invasion reversals owing to multi-point interactions, are also outlined.

The role of institutional incentives and the exemplar in promoting cooperation

People on average do not play their individually rational Nash equilibrium (NE) strategy in game experiments based on the public goods game (PGG) that model social dilemmas. Differences from NE behavior have also been observed in PGG experiments that include incentives to cooperate, especially when these are peer-incentives administered by the players themselves. In our repeated PGG experiment, an institution rewards and punishes individuals based on their contributions. The primary experimental result is that institutions which both reward and punish (IRP) promote cooperation significantly better than either institutions which only punish (IP) or which only reward (IR), and that IP has contribution levels significantly above IR. Although comparing their single-round NE strategies correctly predicts which incentives are best at promoting cooperation, individuals do not play these strategies overall. Our analysis shows that other intrinsic motivations that combine conforming behavior with reactions to being rewarded/punished provide a better explanation of observed outcomes. In our experiments, some individuals who display more cooperation than other individuals can be regarded as the exemplars (or leaders). The role of these exemplars in promoting cooperation provides important insights into understanding cooperation in PGG and the effectiveness of institutional incentives at promoting desirable societal behavior.

Optimal distribution of incentives for public cooperation in heterogeneous interaction environments

In the framework of evolutionary games with institutional reciprocity, limited incentives are at disposal for rewarding cooperators and punishing defectors. In the simplest case, it can be assumed that, depending on their strategies, all players receive equal incentives from the common pool. The question arises, however, what is the optimal distribution of institutional incentives? How should we best reward and punish individuals for cooperation to thrive? We study this problem for the public goods game on a scale-free network. We show that if the synergetic effects of group interactions are weak, the level of cooperation in the population can be maximized simply by adopting the simplest “equal distribution” scheme. If synergetic effects are strong, however, it is best to reward high-degree nodes more than low-degree nodes. These distribution schemes for institutional rewards are independent of payoff normalization. For institutional punishment, however, the same optimization problem is more complex, and its solution depends on whether absolute or degree-normalized payoffs are used. We find that degree-normalized payoffs require high-degree nodes be punished more lenient than low-degree nodes. Conversely, if absolute payoffs count, then high-degree nodes should be punished stronger than low-degree nodes.

Resource heterogeneity can facilitate cooperation

Although social structure is known to promote cooperation, by locally exposing selfish agents to their own deeds, studies to date assumed that all agents have access to the same level of resources. This is clearly unrealistic. Here we find that cooperation can be maintained when some agents have access to more resources than others. Cooperation can then emerge even in populations in which the temptation to defect is so strong that players would act fully selfishly if their resources were distributed uniformly. Resource heterogeneity can thus be crucial for the emergence and maintenance of cooperation. We also show that resource heterogeneity can hinder cooperation once the temptation to defect is significantly lowered. In all cases, the level of cooperation can be maximized by managing resource heterogeneity.

Differences in resource availability or inequality of wealth are common both in nature and in human societies. Here the authors find that such inequality facilitates cooperation when the generation of public goods is inefficient, but hinders cooperation when the efficiency of joint actions is high.

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.

Evolutionary prisoner's dilemma on evolving random networks

In this paper, we investigate the evolution of cooperation in the spatial prisoner's dilemma game by incorporating partner choice into the framework of evolutionary game theory. Our research shows that the introduction of partner choice can notably promote the cooperative behavior in the prisoner's dilemma game. All the players are more likely to play the game with cooperators, which makes it easier for cooperators to form alliances. In particular, the system will be dominated completely by cooperators in a comfortable environment (i.e., with lower survival cost) because the cooperators can get more benefits than the defectors in this case due to their good reputation. In addition, we have found that the sustenance of cooperators improves notably as well in the snowdrift game and the stag-hunt game due to this introduction.

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.