Conditional strategies and the evolution of cooperation in spatial public goods games

Evolutionary dynamics of trust in hierarchical populations with varying investment strategies

Trust is one of the fundamental elements in the development of human societies, which can be modelled on the trust game. In the traditional trust game, investors decide whether to invest or not, and trustees choose whether to be trustworthy or not. In this study, we differentiate between investors and trustees and assume that strategy imitation only happens among individuals of the same class, in which their ratios remain constant. Trustees can choose to be either trustworthy or untrustworthy, while investors decide between an active and a conservative investment strategies based on environmental factors. Here, the environmental factor is closely related to the number of trustworthy trustees within the group. Applying evolutionary game theory, we investigate behavioural changes in the [Formula: see text]-player trust game when environmental factors are introduced. Our findings indicate that investors can form effective coalitions with trustworthy trustees, thereby excluding untrustworthy ones. Furthermore, we validate the robustness of our model and reveal that different investment behaviours have different advantages under specific environmental conditions. This study highlights the subtle interplay between trust and investment dynamics in different environments, providing new insights into the mechanisms of trust in socioeconomic systems, which has some practical significance.

Promoting cooperation in the voluntary prisoner's dilemma game via reinforcement learning

Reinforcement learning technology has been empirically demonstrated to facilitate cooperation in game models. However, traditional research has primarily focused on two-strategy frameworks (cooperation and defection), which inadequately captures the complexity of real-world scenarios. To address this limitation, we integrated Q-learning into the prisoner's dilemma game, incorporating three strategies: cooperation, defection, and going it alone. We defined each agent's state based on the number of neighboring agents opting for cooperation and included social payoff in the Q-table update process. Numerical simulations indicate that this framework significantly enhances cooperation and average payoff as the degree of social-attention increases. This phenomenon occurs because social payoff enables individuals to move beyond narrow self-interest and consider broader social benefits. Additionally, we conducted a thorough analysis of the mechanisms underlying this enhancement of cooperation.

Evolutionary multi-agent reinforcement learning in group social dilemmas

Reinforcement learning (RL) is a powerful machine learning technique that has been successfully applied to a wide variety of problems. However, it can be unpredictable and produce suboptimal results in complicated learning environments. This is especially true when multiple agents learn simultaneously, which creates a complex system that is often analytically intractable. Our work considers the fundamental framework of Q-learning in public goods games, where RL individuals must work together to achieve a common goal. This setting allows us to study the tragedy of the commons and free-rider effects in artificial intelligence cooperation, an emerging field with potential to resolve challenging obstacles to the wider application of artificial intelligence. While this social dilemma has been mainly investigated through traditional and evolutionary game theory, our work connects these two approaches by studying agents with an intermediate level of intelligence. We consider the influence of learning parameters on cooperation levels in simulations and a limiting system of differential equations, as well as the effect of evolutionary pressures on exploration rate in both of these models. We find selection for higher and lower levels of exploration, as well as attracting values, and a condition that separates these in a restricted class of games. Our work enhances the theoretical understanding of recent techniques that combine evolutionary algorithms with Q-learning and extends our knowledge of the evolution of machine behavior in social dilemmas.

Evolution of cooperation with early social influence for explaining collective action

The logic of collective action has laid a foundation for the research of public choice, and the success of collective action has been a long-term discussion when free-riding mechanism is considered in the dynamics. This study proposes a , which provides a novel dimension for explaining the logic of collective action. Under the framework, the accumulation of early social influence, conformity, and the pressure of relationship updating in small groups is discussed. The experiment results show that the accumulation of early social influence indirectly promotes the participants of collective action; conformity is conducive to stimulating collective action, but relies on the accumulation of early social influence; the pressure of relationship updating plays the small-group role, which promotes the participation of collective actions; all these effects are helpful in forming the cascade of cooperators, and prevent the coexistence of participants and non-participants of collective action.

Evolution of cooperation in heterogeneous populations with asymmetric payoff distribution

The emergence and maintenance of cooperation is a complex and intriguing issue, especially in the context of widespread asymmetries in interactions that arise from individual differences in real-world scenarios. This study investigates how asymmetric payoff distribution affects cooperation in public goods games by considering a population composed of two types of individuals: strong and weak. The asymmetry is reflected in the fact that strong players receive a larger share of the public pool compared to weak players. Our results demonstrate that asymmetric payoff distribution can promote cooperation in well-mixed populations and trigger the co-evolution of cooperation between sub-populations of strong and weak players. In structured populations, however, the effect of asymmetric payoff distribution on cooperation is contingent on the proportion of strong players and the extent of their payoff share, which can either foster or inhibit cooperation. By adjusting the interaction probability between strong and weak players based on their spatial arrangement on lattice networks, we find that moderate interaction probabilities most effectively maintain cooperation. This study provides valuable insights into the dynamics of cooperation under asymmetric conditions, highlighting the complex role of asymmetrical interactions in the evolution of cooperation.

Threshold incentive mechanisms for the sustainable management of public resources

Maintaining global ecological balance is inextricably linked to the effective governance of public resources. Previous studies have proposed the introduction of incentive mechanisms to mitigate the defection behavior within the scope of public resource management to facilitate sustainable utilization. However, these incentive strategies often present a considerable financial burden. Here, we first propose a two-threshold incentive scheme based on group state objectives, where the reward mechanism is triggered when the number of cooperators is below the threshold M, and the punishment mechanism is triggered when the number of cooperators is above the threshold Q. We further introduce an incentive mechanism by considering both resource and group thresholds, where incentives are implemented separately when the number of cooperators and the current quantity of resources meet thresholds. Our theoretical results reveal that introducing these two new mechanisms can effectively maintain cooperative behavior and sustainable resources while reducing management costs. However, if the initial resource level is low, the tragedy of the commons will still occur. It is recommended that the number of developers be reduced, the allocation be lowered, or the development simply suspended and the natural regeneration of resources be waited for.

Herd behavior in public goods games

The problem of free-riding arises when individuals benefit from a shared resource, service, or public good without contributing proportionately to its provision. This conduct often leads to a collective action problem, as individuals pursue personal gains while relying on the contributions of others. In this study, we present a Bayesian inference model to elucidate the behavior of participants in a public goods game, a conceptual framework that captures the essence of the free-riding problem. Here, individuals possess information on the distribution of group donations to the public good. Our model is grounded in the premise that individuals strive to harmonise their actions with the group's donation patterns. Our model is able to replicate behavioral patterns that resemble those observed in experiments with midsized groups (100 people), but fails to replicate those for larger scales (1000 people). Our results suggest that, in these scenarios, humans prefer imitation and convergence behaviors over profit optimization. These insights contribute to understanding how cooperation is achieved through alignment with group behavior.

Evolution of trust in N-player trust games with loss assessment

Trust plays a crucial role in social and economic interactions, serving as the foundation for social stability and human cooperation. Previous studies have explored the evolution of trust between investors and trustees by constructing trust game models, incorporating factors such as network structure, reputation, and incentives. However, these studies often assume that investors consistently maintain their investment behavior, neglecting the potential influence of the investment environment on investment behavior. To address this gap, we introduce a loss assessment mechanism and construct a trust game model. Specifically, investors first allocate their investment amount to an assessment agency, which divides the amount into two parts according to a certain allocation ratio. One part is used for investment assessment, and the results are fed back to the investors. If the payoff from this portion exceeds the investors' expected value, the remaining amount is invested; otherwise, it is returned to the investors. The results indicate that investors with moderate expectations are more likely to form alliances with trustworthy trustees, thereby effectively promoting the evolution of trust. Conversely, lower or higher expectations yield opposite results. Additionally, we find that as investors' expected values increase, the corresponding allocation ratio should also increase to achieve higher payoffs.

The Unification of Evolutionary Dynamics through the Bayesian Decay Factor in a Game on a Graph

We unify evolutionary dynamics on graphs in strategic uncertainty through a decaying Bayesian update. Our analysis focuses on the Price theorem of selection, which governs replicator(-mutator) dynamics, based on a stratified interaction mechanism and a composite strategy update rule. Our findings suggest that the replication of a certain mutation in a strategy, leading to a shift from competition to cooperation in a well-mixed population, is equivalent to the replication of a strategy in a Bayesian-structured population without any mutation. Likewise, the replication of a strategy in a Bayesian-structured population with a certain mutation, resulting in a move from competition to cooperation, is equivalent to the replication of a strategy in a well-mixed population without any mutation. This equivalence holds when the transition rate from competition to cooperation is equal to the relative strength of selection acting on either competition or cooperation in relation to the selection differential between cooperators and competitors. Our research allows us to identify situations where cooperation is more likely, irrespective of the specific payoff levels. This approach provides new perspectives into the intended purpose of Price's equation, which was initially not designed for this type of analysis.

The emergence of division of labour through decentralized social sanctioning

Human ecological success relies on our characteristic ability to flexibly self-organize into cooperative social groups, the most successful of which employ substantial specialization and division of labour. Unlike most other animals, humans learn by trial and error during their lives what role to take on. However, when some critical roles are more attractive than others, and individuals are self-interested, then there is a social dilemma: each individual would prefer others take on the critical but unremunerative roles so they may remain free to take one that pays better. But disaster occurs if all act thus and a critical role goes unfilled. In such situations learning an optimum role distribution may not be possible. Consequently, a fundamental question is: how can division of labour emerge in groups of self-interested lifetime-learning individuals? Here, we show that by introducing a model of social norms, which we regard as emergent patterns of decentralized social sanctioning, it becomes possible for groups of self-interested individuals to learn a productive division of labour involving all critical roles. Such social norms work by redistributing rewards within the population to disincentivize antisocial roles while incentivizing prosocial roles that do not intrinsically pay as well as others.

Co-evolution of conditional cooperation and social norm

The co-evolution of conditional cooperation and social norms has garnered significant attention, yet the underlying mechanisms remain elusive. Social norms result from empirical expectations, individual expectations of group behavior, and normative expectations, the population's expectations of individual behavior. Aligning these expectations aids in norm formation, but diverse individual reactions to observed behavior and their sensitivity to norm conformity can be challenging. In our study, the agents are initially endowed with diverse conditional expectations, which mirror their anticipations regarding group behavior and their inherent inclination to conform to social norms, indicative of their sensitivity to psychic costs. These agents engage in a repeated public goods game, where their decisions to cooperate are shaped by their conditional expectations and the observed levels of cooperation within their group. Concurrently, free riders experience psychic costs determined by the overall level of cooperation, contribution costs, and the individual's inclination to adhere to social norms. Remarkably, our simulations unveil that agents commencing with random conditional expectations and a propensity to conform to norms can adapt to lower conditional expectations and moderate their propensity to conform to norms when initial cooperation levels are high and the contribution cost is reduced. Interestingly, increasing contribution costs intensify the population's response to norm enforcement, but this doesn't always result in a corresponding increase in cooperation. By incorporating population diversity and accounting for empirical and normative expectations within our model, we gain valuable insights into the intricate relationship between conditional cooperation and the emergence of social norms.

Conformity effect on the evolution of cooperation in signed networks

Human behaviors are often subject to conformity, but little research attention has been paid to social dilemmas in which players are assumed to only pursue the maximization of their payoffs. The present study proposed a generalized prisoner dilemma model in a signed network considering conformity. Simulation shows that conformity helps promote the imitation of cooperative behavior when positive edges dominate the network, while negative edges may impede conformity from fostering cooperation. The logic of homophily and xenophobia allows for the coexistence of cooperators and defectors and guides the evolution toward the equality of the two strategies. We also find that cooperation prevails when individuals have a higher probability of adjusting their relation signs, but conformity may mediate the effect of network adaptation. From a population-wide view, network adaptation and conformity are capable of forming the structures of attractors or repellers.

Indirect exclusion can promote cooperation in repeated group interactions

Social exclusion has been regarded as one of the most effective measures to promote the evolution of cooperation. In real society, the way in which social exclusion works can be direct or indirect. However, thus far there is no related work to explore how indirect exclusion influences the evolution of cooperation from a theoretical perspective. Here, we introduce indirect exclusion into the repeated public goods game where the game organizer probabilistically selects cooperators after the first game round to participate in the following possible game interactions. We then investigate the evolutionary dynamics of cooperation both in infinite and finite well-mixed populations. Through theoretical analysis and numerical calculations, we find that the introduction of indirect exclusion can induce the stable coexistence of cooperators and defectors or the dominance of cooperators, which thus effectively promotes the evolution of cooperation. Besides, we show that the identifying probability of the organizer has a nonlinear effect on public cooperation when its value is lower than an intermediate value, while the higher identifying probability can maintain a high level of cooperation. Furthermore, our results show that increasing the average rounds of game interactions can effectively promote the evolution of cooperation.

Evolution of conditional cooperation in public good games

Cooperation declines in repeated public good games because individuals behave as conditional cooperators. This is because individuals imitate the social behaviour of successful individuals when their payoff information is available. However, in human societies, individuals cooperate in many situations involving social dilemmas. We hypothesize that humans are sensitive to both success (payoffs) and how that success was obtained, by cheating (not socially sanctioned) or good behaviour (socially sanctioned and adds to prestige or reputation), when information is available about payoffs and prestige. We propose and model a repeated public good game with heterogeneous conditional cooperators where an agent's donation in a public goods game depends on comparing the number of donations in the population in the previous round and with the agent's arbitrary chosen conditional cooperative criterion. Such individuals imitate the social behaviour of role models based on their payoffs and prestige. The dependence is modelled by two population-level parameters: affinity towards payoff and affinity towards prestige. These affinities influence the degree to which agents value the payoff and prestige of role models. Agents update their conditional strategies by considering both parameters. The simulations in this study show that high levels of cooperation are established in a population consisting of heterogeneous conditional cooperators for a certain range of affinity parameters in repeated public good games. The results show that social value (prestige) is important in establishing cooperation.

Emergence of social inequality in the spatial harvesting of renewable public goods

Spatially extended ecological public goods, such as forests, grasslands, and fish stocks, are at risk of being overexploited by selfish consumers–a phenomenon widely recognized as the ‘tragedy of the commons.’ The interplay of spatial and ecological dimensions introduces new features absent in non-spatial ecological contexts, such as consumer mobility, local information availability, and strategy evolution through social learning in neighborhoods. It is unclear how these features interact to influence the harvesting and dispersal strategies of consumers. To answer these questions, we develop and analyze an individual-based, spatially structured, eco-evolutionary model with explicit resource dynamics. We report the following findings. (1) When harvesting efficiency is low, consumers evolve a sedentary consumption strategy, through which the resource is harvested sustainably, but with harvesting rates far below their maximum sustainable value. (2) As harvesting efficiency increases, consumers adopt a mobile ‘consume-and-disperse’ strategy, which is sustainable, equitable, and gives maximum sustainable yield. (3) A further increase in harvesting efficiency leads to large-scale overexploitation. (4) If costs of dispersal are significant, increased harvesting efficiency also leads to social inequality between frugal sedentary consumers and overexploitative mobile consumers. Whereas overexploitation can occur without social inequality, social inequality always leads to overexploitation. Thus, we identify four conditions that–while being characteristic of technological progress in modern societies–risk social inequality and overexploitation: high harvesting efficiency, moderately low costs of dispersal, high consumer density, and the tendency of consumers to adopt new strategies rapidly. We also show how access to global information–another feature widespread in modern societies–helps mitigate these risks.

Throughout history, humans have shaped ecological landscapes, which in turn have influenced human behavior. This mutual dependence is epitomized when human consumers harvest a spatially extended renewable resource. Simple models predict that, when multiple consumers harvest a shared resource, each is tempted to harvest faster than his/her peers, putting the resource at risk of overexploitation. It is unclear, however, how the interplay among resource productivity, consumer mobility, and social learning in spatial ecological public goods games influences evolved consumer behavior. Here, using an individual-based, spatially structured, eco-evolutionary model of consumers and a resource, we find that increasing resource productivity initially promotes efficient resource use by enabling mobile consumption strategies, but eventually leads to inequality and overexploitation, as overexploitative mobile consumers coexist with frugal sedentary consumers. When consumers are impatient (i.e., eager to imitate successful strategies) or myopic (i.e., unaware of conditions outside of their neighborhoods), inequality and overexploitation tend to aggravate.

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.

Conditional rehabilitation of cooperation under strategic uncertainty

In order to address the topic of the tragedy of the commons, more specifically that of tropical forest ecosystems explored as common-pool resources endowed with public-good features and exposed to deforestation risks, we consider game-theoretic population dynamics contingent on various differential equations. We propose an evolutionary model handed down to the Price theorem of selection. In a set of model-players evolving in strategic uncertainty and subject to certain mutation toward cooperation, the Price equation evens out unstructured and structured population replicator dynamics. According to the model outputs, avoiding the tragedy of the commons can be achieved on condition that half of the population temporarily exhibits a cooperative behavior. Furthermore, cooperative model-players ought to be rewarded at a level equivalent to the joint selection of cooperators and competitors issued from the unifying Price identity.

Evolutionary Game Model of Information Sharing Behavior in Supply Chain Network With Agent-Based Simulation

In the supply chain network, information sharing between enterprises can produce synergistic effect and improve the benefits. In this article, evolutionary game theory is used to analyse the evolution process of the information sharing behaviour between supply chain network enterprises with different penalties and information sharing risk costs. Analysis and agent-based simulation results show that when the amount of information between enterprises in supply chain networks is very large, it is difficult to form a sharing of cooperation; increase penalties, control cost sharing risk can increase the probability of supply chain information sharing network and shorten the time for information sharing.

Information flows in the market: An evolutionary game approach

Information influences the decisions that investors make in the markets. Whether this information is true or false can be quantified and distinguished by markets. To study how information propagates through markets, we propose an information flow game based on an evolutionary game approach. In reality, investors transmit profits or losses when they transmit information, because there are values associated with information in the market. In the information flow game, information is represented by its value. Investors in the game can choose to be sharers or silencers. Sharers share their information with their neighbors according to a sharing rate α, which is a key quantity in the model. In the evolutionary process, we show that more sharers emerge when the market is full of rumors, especially as the sharing rate increases. Higher values of the sharing rate reduce the standard deviation of the information value in such markets, whereas the opposite occurs in markets that largely consist of true information. The reactions of the investors are asymmetric, which indicates that investors are more sensitive to losses than to profits. Furthermore, as the network becomes more random, a higher sharing rate becomes more beneficial for the stability of the emergence of sharers if information is generally false, whereas a lower sharing rate is helpful for the stability of the emergence of sharers if information is generally true.

Investment preference promotes cooperation in spatial public goods game

It is usually assumed that each cooperator contributes equally to different public pools in spatial public goods game. However, it is more reasonable to invest differently according to individual investment preference. In this paper, an extended public goods game, in which cooperators contribute to the groups according to the investment preference, is developed. The investment preference of a cooperator is characterized by the fraction of the cooperator from his/her own memory about a group and the intensity of investment preference is represented by a tunable parameter α. The well-mixed population and the structured population are analyzed under this mechanism. It is shown that the investment preference can give rise to coordination. Moreover, the extensive numerical simulation results show that with the increasing of investment preference density or memory length, the proportion of cooperation can increase monotonously. This is because the investment preference could help cooperators resist the invasion from defectors. Compared with the basic version, the new mechanism is able to promote cooperation effectively. Our research may provide a valuable insight for further exploring the nature of cooperation in the real world.

The evolution of cooperation in signed networks under the impact of structural balance

Structural balance plays an important role in the dynamics of signed networks. Based on structural balance, we generalize the evolution of cooperation in signed networks. Here we develop a new simulation model to study the impact of structural balance on the evolution of cooperation in signed networks. The simulation shows that cooperation prevails when an individual has a higher probability of adjusting the signs of its relations. We also find that structural balance forces the coexistence of cooperators and defectors, while the initial attributes of networks have little impact on the evolution of cooperation in the presence of structural balance, although they have a strong effect on the evolution of structural balance.

Reciprocity-based cooperative phalanx maintained by overconfident players

According to the evolutionary game theory principle, a strategy representing a higher payoff can spread among competitors. But there are cases when a player consistently overestimates or underestimates her own payoff, which undermines proper comparison. Interestingly, both underconfident and overconfident individuals are capable of elevating the cooperation level significantly. While former players stimulate a local coordination of strategies, the presence of overconfident individuals enhances the spatial reciprocity mechanism. In both cases the propagations of competing strategies are influenced in a biased way resulting in a cooperation supporting environment. These effects are strongly related to the nonlinear character of invasion probabilities which is a common and frequently observed feature of microscopic dynamics.

Seven rules to avoid the tragedy of the commons

Cooperation among self-interested players in a social dilemma is fragile and easily interrupted by mistakes. In this work, we study the repeated n-person public-goods game and search for a strategy that forms a cooperative Nash equilibrium in the presence of implementation error with a guarantee that the resulting payoff will be no less than any of the co-players'. By enumerating strategic possibilities for n=3, we show that such a strategy indeed exists when its memory length m equals three. It means that a deterministic strategy can be publicly employed to stabilize cooperation against error with avoiding the risk of being exploited. We furthermore show that, for general n-person public-goods game, m ≥ n is necessary to satisfy the above criteria.

Evolution of Cooperation with Heterogeneous Conditional Cooperators

Conditional cooperation declines over time if heterogeneous ideal conditional agents are involved in repeated interactions. With strict assumptions of rationality and a population consisting of ideal conditional agents who strictly follow a decision rule, cooperation is not expected. However, cooperation is commonly observed in human societies. Hence, we propose a novel evolutionary agent-based model where agents rely on social information. Each agent interacts only once either as a donor or as a receiver. In our model, the population consists of either non-ideal or ideal heterogeneous conditional agents. Their donation decisions are stochastically based on the comparison between the number of donations in the group and their conditional cooperative criterion value. Non-ideal agents occasionally cooperate even if the conditional rule of the agent is not satisfied. The stochastic decision and selection rules are controlled with decision intensity and selection intensity, respectively. The simulations show that high levels of cooperation (more than 90%) are established in the population with non-ideal agents for a particular range of parameter values. The emergence of cooperation needs non-ideal agents and a heterogeneous population. The current model differs from existing models by relying on social information and not on individual agent's prior history of cooperation.

Evolution of cooperation with interactive identity and diversity

Interactive identity and interactive diversity are generally regarded as two typical interaction patterns in living systems. The former describes that in each generation every individual behaves identically to all of its opponents, and the latter allows each individual to behave diversely to its distinct opponents. Most traditional research on the evolution of cooperation, however, has been confined to populations with a uniform interaction pattern. Here we study the cooperation conundrum in a diverse population comprising players with interactive identity and with interactive diversity. We find that in homogeneous networks a small fraction of players taking interactive diversity are enough to stabilize cooperation for a wide range of payoff values even in a noisy environment. When assigned to heterogeneous networks, players in high-degree nodes taking interactive diversity significantly strengthen systems' resilience against the shifty environment and enlarge the survival region of cooperation. However, they fail to establish a homogeneous strategy 'cloud' in the neighborhood and thus can not coordinate players in low-degree nodes to reach a socially optimal cooperation level. The most favorable outcome emerges when players in high-degree nodes take interactive identity and meanwhile others adopt interactive diversity. Our findings reveal the significance of the two typical interaction patterns and could be a good heuristic in coordinating them to achieve the social optimum in 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.

Reinforcement learning accounts for moody conditional cooperation behavior: experimental results

In social dilemma games, human participants often show conditional cooperation (CC) behavior or its variant called moody conditional cooperation (MCC), with which they basically tend to cooperate when many other peers have previously cooperated. Recent computational studies showed that CC and MCC behavioral patterns could be explained by reinforcement learning. In the present study, we use a repeated multiplayer prisoner's dilemma game and the repeated public goods game played by human participants to examine whether MCC is observed across different types of game and the possibility that reinforcement learning explains observed behavior. We observed MCC behavior in both games, but the MCC that we observed was different from that observed in the past experiments. In the present study, whether or not a focal participant cooperated previously affected the overall level of cooperation, instead of changing the tendency of cooperation in response to cooperation of other participants in the previous time step. We found that, across different conditions, reinforcement learning models were approximately as accurate as a MCC model in describing the experimental results. Consistent with the previous computational studies, the present results suggest that reinforcement learning may be a major proximate mechanism governing MCC behavior.

Cooperation driven by success-driven group formation

In the traditional setup of the public goods game all players are involved in every available group and the mutual benefit is shared among competing cooperator and defector strategies. However, in real life situations the group formation of players could be more sophisticated because not all players are attractive enough for others to participate in a joint venture. What if only those players who are successful enough to the neighbors can initiate a group formation and establish a game? To elaborate this idea we employ a modified protocol and demonstrate that a carefully chosen threshold to establish a joint venture could efficiently improve the cooperation level even if the synergy factor would suggest a full defector state otherwise. The microscopic mechanism that is responsible for this effect is based on the asymmetric consequences of competing strategies: while the success of a cooperator provides a long-time well-being for the neighborhood, the temporary advantage of defection cannot be maintained if the protocol is based on the success of leaders.

Culture and cooperation in a spatial public goods game

We study the coevolution of culture and cooperation by combining the Axelrod model of cultural dissemination with a spatial public goods game, incorporating both noise and social influence. Both participation and cooperation in public goods games are conditional on cultural similarity. We find that a larger "scope of cultural possibilities" in the model leads to the survival of cooperation, when noise is not present, and a higher probability of a multicultural state evolving, for low noise rates. High noise rates, however, lead to both rapid extinction of cooperation and collapse into cultural "anomie," in which stable cultural regions fail to form. These results suggest that cultural diversity can actually be beneficial for the evolution of cooperation, but that cultural information needs to be transmitted accurately in order to maintain both coherent cultural groups and cooperation.

Co-action provides rational basis for the evolutionary success of Pavlovian strategies

Strategies incorporating direct reciprocity, e.g., Tit-for-Tat and Pavlov, have been shown to be successful for playing the Iterated Prisoners Dilemma (IPD), a paradigmatic problem for studying the evolution of cooperation among non-kin individuals. However it is an open question whether such reciprocal strategies can emerge as the rational outcome of repeated interactions between selfish agents. Here we show that adopting a co-action perspective, which takes into account the symmetry between agents - a relevant consideration in biological and social contexts - naturally leads to such a strategy. For a 2-player IPD, we show that the co-action solution corresponds to the Pavlov strategy, thereby providing a rational basis for it. For an IPD involving many players, an instance of the Public Goods game where cooperation is generally considered to be harder to achieve, we show that the cooperators always outnumber defectors in the co-action equilibrium. This can be seen as a generalization of Pavlov to contests involving many players. In general, repeated interactions allow rational agents to become aware of the inherent symmetry of their situation, enabling them to achieve robust cooperation through co-action strategies - which, in the case of IPD, is a reciprocal Pavlovian one.

Does information about others’ behavior undermine cooperation in social dilemmas?

This project addresses how and why behavior in a resource dilemma differs when one only knows the choices of others versus only knows the state of the resource. Study 1 suggested that resource information is more valuable than social information, in that if the resource can be monitored, whether or not others’ choices can also be monitored has no impact on behavior. However, if the state of the resource is not known, the ability to know what others are doing is critical for cooperation. This seems to be because resource information encourages planning and long-term thinking, and social information encourages comparative thinking. Study 2 replicated the behavior pattern, revealed—surprisingly—that warnings that a resource is critically low undermine (rather than promote) cooperation, and that such responses depend on the availability of social and environmental information. Discussion focuses on how incomplete information about a resource might be addressed.

Evolution of conditional cooperation under multilevel selection

We study the emergence of conditional cooperation in the presence of both intra-group and inter-group selection. Individuals play public goods games within their groups using conditional strategies, which are represented as piecewise linear response functions. Accordingly, groups engage in conflicts with a certain probability. In contrast to previous studies, we consider continuous contribution levels and a rich set of conditional strategies, allowing for a wide range of possible interactions between strategies. We find that the existence of conditional strategies enables the stabilization of cooperation even under strong intra-group selection. The strategy that eventually dominates in the population has two key properties: (i) It is unexploitable with strong intra-group selection; (ii) It can achieve full contribution to outperform other strategies in the inter-group selection. The success of this strategy is robust to initial conditions as well as changes to important parameters. We also investigate the influence of different factors on cooperation levels, including group conflicts, group size, and migration rate. Their effect on cooperation can be attributed to and explained by their influence on the relative strength of intra-group and inter-group selection.

Threshold Games and Cooperation on Multiplayer Graphs

Objective

The study investigates the effect on cooperation in multiplayer games, when the population from which all individuals are drawn is structured—i.e. when a given individual is only competing with a small subset of the entire population.

Method

To optimize the focus on multiplayer effects, a class of games were chosen for which the payoff depends nonlinearly on the number of cooperators—this ensures that the game cannot be represented as a sum of pair-wise interactions, and increases the likelihood of observing behaviour different from that seen in two-player games. The chosen class of games are named “threshold games”, and are defined by a threshold, M > 0, which describes the minimal number of cooperators in a given match required for all the participants to receive a benefit. The model was studied primarily through numerical simulations of large populations of individuals, each with interaction neighbourhoods described by various classes of networks.

Results

When comparing the level of cooperation in a structured population to the mean-field model, we find that most types of structure lead to a decrease in cooperation. This is both interesting and novel, simply due to the generality and breadth of relevance of the model—it is likely that any model with similar payoff structure exhibits related behaviour. More importantly, we find that the details of the behaviour depends to a large extent on the size of the immediate neighbourhoods of the individuals, as dictated by the network structure. In effect, the players behave as if they are part of a much smaller, fully mixed, population, which we suggest an expression for.

Corruption and the Other(s): Scope of Superordinate Identity Matters for Corruption Permissibility

The decision to engage in corruption-public and private corruption, nepotism, and embezzlement-is often attributed to rational actors maximizing benefits to themselves. However, the importance of reciprocal relationships in humans suggests that an actor may weigh the costs of harms of her corrupt behavior to individuals who may generate future benefits for her. We hypothesize that actors who have a larger circle of actual and potential social partners will have more individuals to consider when generating harms and will thus be less likely to find corrupt acts permissible than actors with smaller circles of valued others. Using data from the World Values Survey and European Values Study (WVS), we explore whether participants with a larger geographic identity or a greater number of group memberships (i.e. a larger scope of actual and potential social partners) are less likely to find accepting bribes permissible. We find mixed support for our hypotheses, but consistently find that WVS participants with local, country, continent, or world geographic identities are less likely to find accepting a bribe permissible than those with regional identities-that is, actors whose primary identities that encompass more than their region find corruption less permissible. We discuss the importance of considering an actor's valuation of others when modeling corruption persistence, noting that establishing scopes of positive valuation is a precursor to predicting where actors will target benefits and shunt costs.

Benefits of tolerance in public goods games

Leaving the joint enterprise when defection is unveiled is always a viable option to avoid being exploited. Although loner strategy helps the population not to be trapped into the tragedy of the commons state, it could offer only a modest income for nonparticipants. In this paper we demonstrate that showing some tolerance toward defectors could not only save cooperation in harsh environments but in fact results in a surprisingly high average payoff for group members in public goods games. Phase diagrams and the underlying spatial patterns reveal the high complexity of evolving states where cyclic dominant strategies or two-strategy alliances can characterize the final state of evolution. We identify microscopic mechanisms which are responsible for the superiority of global solutions containing tolerant players. This phenomenon is robust and can be observed both in well-mixed and in structured populations highlighting the importance of tolerance in our everyday life.

Evolutionary game theory: cells as players

In two papers we review game theory applications in biology below the level of cognitive living beings. It can be seen that evolution and natural selection replace the rationality of the actors appropriately. Even in these micro worlds, competing situations and cooperative relationships can be found and modeled by evolutionary game theory. Also those units of the lowest levels of life show different strategies for different environmental situations or different partners. We give a wide overview of evolutionary game theory applications to microscopic units. In this first review situations on the cellular level are tackled. In particular metabolic problems are discussed, such as ATP-producing pathways, secretion of public goods and cross-feeding. Further topics are cyclic competition among more than two partners, intra- and inter-cellular signalling, the struggle between pathogens and the immune system, and the interactions of cancer cells. Moreover, we introduce the theoretical basics to encourage scientists to investigate problems in cell biology and molecular biology by evolutionary game theory.

Social exclusion in finite populations

Social exclusion, keeping free riders from benefit sharing, plays an important role in sustaining cooperation in our world. Here we propose two different exclusion regimes, namely, peer exclusion and pool exclusion, to investigate the evolution of social exclusion in finite populations. In the peer exclusion regime, each excluder expels all the defectors independently, and thus bears the total cost on his own, while in the pool exclusion regime, excluders spontaneously form an institution to carry out rejection of the free riders, and each excluder shares the cost equally. In a public goods game containing only excluders and defectors, it is found that peer excluders outperform pool excluders if the exclusion costs are small, and the situation is converse once the exclusion costs exceed some critical points, which holds true for all the selection intensities and different update rules. Moreover, excluders can dominate the whole population under a suitable parameters range in the presence of second-order free riders (cooperators), showing that exclusion has prominent advantages over common costly punishment. More importantly, our finding indicates that the group exclusion mechanism helps the cooperative union to survive under unfavorable conditions. Our results may give some insights into better understanding the prevalence of such a strategy in the real world and its significance in sustaining cooperation.

Dependency links can hinder the evolution of cooperation in the prisoner's dilemma game on lattices and networks

Networks with dependency links are more vulnerable when facing the attacks. Recent research also has demonstrated that the interdependent groups support the spreading of cooperation. We study the prisoner's dilemma games on spatial networks with dependency links, in which a fraction of individual pairs is selected to depend on each other. The dependency individuals can gain an extra payoff whose value is between the payoff of mutual cooperation and the value of temptation to defect. Thus, this mechanism reflects that the dependency relation is stronger than the relation of ordinary mutual cooperation, but it is not large enough to cause the defection of the dependency pair. We show that the dependence of individuals hinders, promotes and never affects the cooperation on regular ring networks, square lattice, random and scale-free networks, respectively. The results for the square lattice and regular ring networks are demonstrated by the pair approximation.

Asymmetric interaction paired with a super-rational strategy might resolve the tragedy of the commons without requiring recognition or negotiation

Avoiding the tragedy of the commons requires that one or more individuals in a group or partnership “volunteer”, benefiting the group at a cost to themselves. Recognition and negotiation with social partners can maintain cooperation, but are often not possible. If recognition and negotiation are not always the mechanism by which cooperative partnerships avoid collective tragedies, what might explain the diverse social cooperation observed in nature? Assuming that individuals interact asymmetrically and that both “weak” and “strong” players employ a super-rational strategy, we find that tragedy of the commons can be avoided without requiring either recognition or negotiation. Whereas in the volunteer's dilemma game a rational “strong” player is less likely to volunteer to provide a common good in larger groups, we show that under a wide range of conditions a super-rational “strong” player is more likely to provide a common good. These results imply that the integration of super-rationality and asymmetric interaction might have the potential to resolve the tragedy of the commons. By illuminating the conditions under which players are likely to volunteer, we shed light on the patterns of volunteerism observed in variety of well-studied cooperative social systems, and explore how societies might avert social tragedies.

Aspiration-based partner switching boosts cooperation in social dilemmas

Most previous studies concerning linking dynamics often assumed that links pairing individuals should be identified and treated differently during topology adjusting procedure, in order to promote cooperation. A common assumption was that cooperators were expected to avoid being exploited by quickly breaking up relationships with defectors. Then the so-called prosocial links linking two cooperators (abbreviated as CC links hereafter) would be much favored by evolution, whereby cooperation was promoted. However, we suggest that this is not always necessary. Here, we developed a minimal model in which an aspiration-based partner switching mechanism was embedded to regulate the evolution of cooperation in social dilemmas. Individuals adjusted social ties in a self-questioning manner in line with the learning theory. Less game information was involved during dynamic linking and all links were tackled anonymously irrespective of their types (i.e., CD links, DD links, or CC links). The main results indicate that cooperation flourishes for a broad range of parameters. The denser the underlying network, the more difficult the evolution of cooperation. More importantly, moderate aspirations do much better in promoting the evolution of altruistic behavior and for most cases there exists the optimal aspiration level that most benefits cooperation. Too strong or too weak selection intensity turns out to be pretty conducive to the evolution of cooperation in such a dynamical system.

Social dilemma alleviated by sharing the gains with immediate neighbors

We study the evolution of cooperation in the evolutionary spatial prisoner's dilemma game (PDG) and snowdrift game (SG), within which a fraction α of the payoffs of each player gained from direct game interactions is shared equally by the immediate neighbors. The magnitude of the parameter α therefore characterizes the degree of the relatedness among the neighboring players. By means of extensive Monte Carlo simulations as well as an extended mean-field approximation method, we trace the frequency of cooperation in the stationary state. We find that plugging into relatedness can significantly promote the evolution of cooperation in the context of both studied games. Unexpectedly, cooperation can be more readily established in the spatial PDG than that in the spatial SG, given that the degree of relatedness and the cost-to-benefit ratio of mutual cooperation are properly formulated. The relevance of our model with the stakeholder theory is also briefly discussed.

Direct sum matrix game with prisoner's dilemma and snowdrift game

A direct sum form is proposed for constructing a composite game from two 2 x 2 games, prisoner's dilemma and snowdrift game. This kind of direct sum form game is called a multiple roles game. The replicator dynamics of the multiple roles game with will-mixed populations is explored. The dynamical behaviors on square lattice are investigated by numerical simulation. It is found that the dynamical behaviors of population on square lattice depend on the mixing proportion of the two simple games. Mixing SD activities to pure PD population inhibits the proportion of cooperators in PD, and mixing PD activities to pure SD population stimulates the proportion of cooperators in SD. Besides spatial reciprocity, our results show that there are roles reciprocities between different types of individuals.

Difference of reciprocity effect in two coevolutionary models of presumed two-player and multiplayer games

Unlike other natural network systems, assortativity can be observed in most human social networks; however, it has been reported that a social dilemma situation represented by a 2×2 prisoner's dilemma game favors dissortativity to enhance cooperation. Our simulations successfully reveal that a public goods game with coevolution for both agents' strategy and network topology encourages assortativity, although it only slightly enhances cooperation as compared to a 2×2 donor and recipient game with a strong dilemma to be solved. This outcome occurs because the network dynamics in a multiplayer game discourages emerging cooperation unlike its beneficial result in a 2×2 prisoner's dilemma game.

Decelerated invasion and waning-moon patterns in public goods games with delayed distribution

We study the evolution of cooperation in the spatial public goods game, focusing on the effects that are brought about by the delayed distribution of goods that accumulate in groups due to the continuous investments of cooperators. We find that intermediate delays enhance network reciprocity because of a decelerated invasion of defectors, who are unable to reap the same high short-term benefits as they do in the absence of delayed distribution. Long delays, however, introduce a risk because the large accumulated wealth might fall into the wrong hands. Indeed, as soon as the curvature of a cooperative cluster turns negative, the engulfed defectors can collect the heritage of many generations of cooperators and by doing so start a waning-moon pattern that nullifies the benefits of decelerated invasion. Accidental meeting points of growing cooperative clusters may also act as triggers for the waning-moon effect, thus linking the success of cooperators with their propensity to fail in a rather bizarre way. Our results highlight that "investing in the future" is a good idea only if that future is sufficiently near and not likely to be burdened by inflation.

Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas

We show that the resolution of social dilemmas in random graphs and scale-free networks is facilitated by imitating not the strategy of better-performing players but, rather, their emotions. We assume sympathy and envy to be the two emotions that determine the strategy of each player in any given interaction, and we define them as the probabilities of cooperating with players having a lower and a higher payoff, respectively. Starting with a population where all possible combinations of the two emotions are available, the evolutionary process leads to a spontaneous fixation to a single emotional profile that is eventually adopted by all players. However, this emotional profile depends not only on the payoffs but also on the heterogeneity of the interaction network. Homogeneous networks, such as lattices and regular random graphs, lead to fixations that are characterized by high sympathy and high envy, while heterogeneous networks lead to low or modest sympathy but also low envy. Our results thus suggest that public emotions and the propensity to cooperate at large depend, and are in fact determined by, the properties of the interaction network.