Reputation-based partner choice promotes cooperation in social networks

Partner perceptions during brief online interactions shape partner selection and cooperation

Evolutionary theory suggests that partner selection - the ability to identify and preferentially interact with individuals willing (warmth) and able (competence) to work towards mutual benefits - is a key driver of cooperative behavior. However, partner selection is complex, requiring the integration of various information, such as impression formation and task affordances. Despite its importance, there is limited research on the effect of these factors on partner selection for cooperative tasks. Thus, this paper investigates how person perceptions (warmth and competence), task affordances, and facial and acoustic nonverbal behavior inform partner selection for cooperative tasks. For this purpose, we asked participants to select partners for a task that either expressed warmth- or competence-related traits. Participants had a 3-minute (online) conversation with up to five individuals, reported their evaluations, selected partners for the task, and then engaged in the task. Results indicate that person perceptions guide partner selection, with each trait being more predictive in relevant tasks. Additionally, we found that the perceptions of warmth, but not competence, can be predicted by facial and acoustic cues during conversations. Lastly, we find that in the context of online social interactions, individuals were more cooperative towards selected participants than unselected. We discuss these implications in the context of the theory of partner selection and offer insights on how these results can be used in future efforts for designing socially intelligent artificial systems that support partner selection decisions.

Spatial reciprocity under reinforcement learning mechanism

At present, the research on the dynamics of cooperative behavior of agents under reinforcement learning mechanism either assumes that agents have global interaction, that is, agents interact with all other agents in the population, or directly study the influence of relevant factors on cooperation evolution based on the local interaction in a network structure. It neglects to formally study how the limitation of agents that only interact with local agents affects their strategy choice. Thus, in this paper, we study the cooperative behavior of agents in a typical social decision-making environment with conflicts between individual interests and collective interests. On the one hand, a programmed game model in game theory, namely, prisoner's dilemma game, is used to capture the essence of real-world dilemmas. On the other hand, the effects of local and global strategy learning on the cooperative evolution of agents are investigated separately, and the nature of spatial reciprocity under the reinforcement learning mechanism is found. Specifically, when there is no inherent connection between the interacting agents and the learning agents within the system, the network structure has a limited effect on promoting cooperation. It is only when there is an overlap between the interacting agents and the learning agents that the spatial reciprocity effect observed in the traditional evolutionary game theory can be fully realized.

A neurocognitive mechanism for increased cooperation during group formation

How do group size changes influence cooperation within groups? To examine this question, we performed a dynamic, network-based prisoner's dilemma experiment with fMRI. Across 83 human participants, we observed increased cooperation as group size increased. However, our computational modeling analysis of behavior and fMRI revealed that groups size itself did not increase cooperation. Rather, interaction between (1) participants' stable prosocial tendencies, and (2) dynamic reciprocal strategy weighed by memory confidence, underlies the group size-modulated increase in cooperation because the balance between them shifts towards the prosocial tendency with higher memory demands in larger groups. We found that memory confidence was encoded in fusiform gyrus and precuneus, whereas its integration with prosocial tendencies was reflected in the left DLPFC and dACC. Therefore, interaction between recall uncertainty during reciprocal interaction (i.e., forgetting) and one's individual prosocial preference is a core pillar of emergent cooperation in more naturalistic and dynamic group formation.

Cultural tightness and resilience against environmental shocks in nonindustrial societies

With climate change intensifying, building resilience against climate-related shocks is now a global imperative. Historically, many societies have faced natural hazards, with some adapting through specific social and cultural practices. Understanding these responses is key to developing modern sustainability strategies. Here, we address this issue by developing a mathematical model explicitly accounting for various environmental shock dimensions, cooperative activities common in nonindustrial societies, and decision-making based on material factors as well as personal values and social norms. Our results suggest that cultural looseness can be vital for effectively responding to mild, slow-onset shocks, leading to moderate cooperation and minimal cultural change. Conversely, coping with severe shocks requires an intermediate level of cultural tightness, fostering significant cultural transformation and high cooperation. While tight societies struggle with new shocks, they may handle regular, severe, fast-onset shocks better than do loose societies. Our research enhances understanding of environmental impacts on cooperation, cultural tightness, and social resilience, and highlights cultural adaptations useful in addressing current environmental challenges like global warming, floods, tornadoes, and soil degradation.

Limited trust in social network games

We consider agents in a social network competing to be selected as partners in collaborative, mutually beneficial activities. We study this through a model in which an agent i can initiate a limited number k_{i}>0 of games and selects partners from its one-hop neighborhood. Each agent can accept as many games offered by its neighbors. Each game signifies a productive joint activity, and the players attempt to maximize their individual utilities. Unsurprisingly, more trustworthy agents, as measured by the game-theoretic concept of limited-trust, are more desirable as partners. Agents learn about their neighbors' trustworthiness through interactions and their behaviors evolve in response. Empirical trials conducted on realistic social networks show that when given the option, many agents become highly trustworthy; most or all become highly trustworthy when knowledge of their neighbors' trustworthiness is based on past interactions rather than known a priori. This trustworthiness is not the result of altruism; instead, agents are intrinsically motivated to become trustworthy partners by competition. Two insights are presented: First, trustworthy behavior drives an increase in the utility of all agents, where maintaining a relatively minor level of trustworthiness may easily improve net utility by as much as 14.5%. If only one agent exhibits a small degree of trustworthiness among self-centered ones, then it can increase its personal utility by up to 25% in certain cases. Second, and counterintuitively, when partnership opportunities are abundant, agents become less trustworthy.

Temporal interaction and its role in the evolution of cooperation

This research investigates the impact of dynamic, time-varying interactions on cooperative behavior in social dilemmas. Traditional research has focused on deterministic rules governing pairwise interactions, yet the impact of interaction frequency and synchronization in groups on cooperation remains underexplored. Addressing this gap, our work introduces two temporal interaction mechanisms to model the stochastic or periodic participation of individuals in public goods games, acknowledging real-life variances due to exogenous temporal factors and geographical time differences. We consider that the interaction state significantly influences both game payoff calculations and the strategy updating process, offering new insights into the emergence and sustainability of cooperation. Our results indicate that maximum game participation frequency is suboptimal under a stochastic interaction mechanism. Instead, an intermediate activation probability maximizes cooperation, suggesting a vital balance between interaction frequency and inactivity security. Furthermore, local synchronization of interactions within specific areas is shown to be beneficial, as time differences hinder the spread of cross-structures but promote the formation of dense cooperative clusters with smoother boundaries. We also note that stronger clustering in networks, larger group sizes, and lower noise increase cooperation. This research contributes to understanding the role of node-based temporality and probabilistic interactions in social dilemmas, offering insights into fostering cooperation.

Cooperation and social organization depend on weighing private and public reputations

To avoid exploitation by defectors, people can use past experiences with others when deciding to cooperate or not ('private information'). Alternatively, people can derive others' reputation from 'public' information provided by individuals within the social network. However, public information may be aligned or misaligned with one's own private experiences and different individuals, such as 'friends' and 'enemies', may have different opinions about the reputation of others. Using evolutionary agent-based simulations, we examine how cooperation and social organization is shaped when agents (1) prioritize private or public information about others' reputation, and (2) integrate others' opinions using a friend-focused or a friend-and-enemy focused heuristic (relying on reputation information from only friends or also enemies, respectively). When agents prioritize public information and rely on friend-and-enemy heuristics, we observe polarization cycles marked by high cooperation, invasion by defectors, and subsequent population fragmentation. Prioritizing private information diminishes polarization and defector invasions, but also results in limited cooperation. Only when using friend-focused heuristics and following past experiences or the recommendation of friends create prosperous and stable populations based on cooperation. These results show how combining one's own experiences and the opinions of friends can lead to stable and large-scale cooperation and highlight the important role of following the advice of friends in the evolution of group cooperation.

The impact of dynamic linking on cooperation on complex networks

In complex social systems, individual relationships and the surrounding environment are constantly changing, allowing individuals to interact on dynamic networks. This study aims to investigate how individuals in a dynamic network engaged in a prisoner's dilemma game adapt their competitive environment through random edge breaks and reconnections when faced with incomplete information and adverse local conditions, thereby influencing the evolution of cooperative behavior. We find that random edge breaks and reconnections in dynamic networks can disrupt cooperative clusters, significantly hindering the development of cooperation. This negative impact becomes more pronounced over larger time scales. However, we also observe that nodes with higher degrees of connectivity exhibit greater resilience to this cooperation disruption. Our research reveals the profound impact of dynamic network structures on the evolution of cooperation and provides new insights into the mechanisms of cooperation in complex systems.

Two-stage strategy update rule based on learning cost in weak prisoner's dilemma

When players are dissatisfied with their actual payoffs, they will change the actuality by learning strategy of neighbors. The more effort players put in, the more likely they are to succeed in learning. Inspired by this, this paper proposes a two-stage strategy update rule based on learning cost. The players first decide whether to learn strategy according to the updating willingness. If the players imitate the strategy of neighbors, they need to pay the learning cost. Results show that for the well-mixed population, if the updating willingness is homogeneous and remains unchanged, reducing the updating willingness or increasing the learning cost can extend the life cycle of cooperators. If the updating willingness is heterogeneous and dynamically adjusted based on the difference between the actual payoff and the expected payoff, increasing aspiration value and learning cost promotes cooperation. For the structured population, if the updating willingness is homogeneous and remains unchanged, the moderate learning cost is beneficial for cooperators to resist the temptation of defection, and reducing updating willingness makes the system maintain cooperation within a larger parameter range. If the updating willingness is heterogeneous and dynamically adjusted, the larger learning cost and the appropriate aspiration value promote cooperation. This study highlights the complex dynamics of cooperation in paid strategy learning, contributing to the theory of cooperation in the evolutionary game.

Can institutions foster cooperation by wealth redistribution?

Theoretical models prescribe how institutions can promote cooperation in a population by imposing appropriate punishments or rewards on individuals. However, many real-world institutions are not sophisticated or responsive enough to ensure cooperation by calibrating their policies. Or, worse yet, an institution might selfishly exploit the population it governs for its own benefit. Here, we study the evolution of cooperation in the presence of an institution that is autonomous, in the sense that it has its own interests that may or may not align with those of the population. The institution imposes a tax on the population and redistributes a portion of the tax revenue to cooperators, withholding the remaining revenue for itself. The institution adjusts its rates of taxation and redistribution to optimize its own long-term, discounted utility. We consider three types of institutions with different goals, embodied in their utility functions. We show that a prosocial institution, whose goal is to maximize the average payoff of the population, can indeed promote cooperation-but only if it is sufficiently forward-looking. On the other hand, an institution that seeks to maximize welfare among cooperators alone will successfully promote collective cooperation even if it is myopic. Remarkably, even a selfish institution, which seeks to maximize the revenue it withholds for itself, can nonetheless promote cooperation. The average payoff of the population increases when a selfish institution is more forward-looking, so that a population under a selfish regime can sometimes fare better than under anarchy. Our analysis highlights the potential benefits of institutional wealth redistribution, even when an institution does not share the interests of the population it governs.

Hostility prevents the tragedy of the commons in metapopulation with asymmetric migration: A lesson from queenless ants

A colony of the queenless ant species, Pristomyrmex punctatus, can broadly be seen as consisting of small-body sized worker ants and relatively larger body-sized cheater ants. Hence, in the presence of intercolony migration, a set of constituent colonies act as a metapopulation exclusively composed of cooperators and defectors. Such a setup facilitates an evolutionary game-theoretic replication-selection model of population dynamics of the ants in a metapopulation. Using the model, we analytically probe the effects of territoriality induced hostility. Such hostility in the ant metapopulation proves to be crucial in preventing the tragedy of the commons, specifically, the workforce, a social good formed by cooperation. This mechanism applies to any metapopulation-not necessarily the ants-composed of cooperators and defectors where interpopulation migration occurs asymmetrically, i.e., cooperators and defectors migrate at different rates. Furthermore, our model validates that there is evolutionary benefit behind the queenless ants' behavior of showing more hostility towards the immigrants from nearby colonies than those from the far-off ones. In order to calibrate our model's parameters, we have extensively used the data available on the queenless ant species, P. punctatus.

Heterogeneous decision-making dynamics of threshold-switching agents on complex networks

In the classical two-player decision-making scenario, individuals may have different tendencies to take a certain action, given that there exists a sufficient number of neighbors adopting a particular option. This is ubiquitous in many real-life contexts including traffic congestion, crowd evacuation, and minimal vertex cover problem. Under best-response dynamics, we investigate the decision-making behaviors of heterogeneous agents on complex networks. Results of the networked games are twofold: for networks of uniform degree distribution (e.g., the lattice) and fraction of the strategy is of a linear function of the threshold setting. Moreover, the equilibrium analysis is provided and the relationship between the equilibrium dynamics and the change of the threshold value is given quantitatively. Next, if the games are played on networks with non-uniform degree distribution (e.g., random regular and scale-free networks), influence of the threshold-switching will be weakened. Robust experiments indicate that it is not the value of the average degree, but the degree distribution that influences how the strategy evolves affected by the threshold settings. Our result shows that the decision-making behaviors can be effectively manipulated by tuning the parameters in the utility function (i.e., thresholds) of some agents for more regular network structures.

Reputations for treatment of outgroup members can prevent the emergence of political segregation in cooperative networks

Reputation systems promote cooperation and tie formation in social networks. But how reputations affect cooperation and the evolution of networks is less clear when societies are characterized by fundamental, identity-based, social divisions like those centered on politics in the contemporary U.S. Using a large web-based experiment with participants (N = 1073) embedded in networks where each tie represents the opportunity to play a dyadic iterated prisoners' dilemma, we investigate how cooperation and network segregation varies with whether and how reputation systems track behavior toward members of the opposing political party (outgroup members). As predicted, when participants know others' political affiliation, early cooperation patterns show ingroup favoritism. As a result, networks become segregated based on politics. However, such ingroup favoritism and network-level political segregation is reduced in conditions in which participants know how others behave towards participants from both their own party and participants from the other party. These findings have implications for our understanding of reputation systems in polarized contexts.

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.

Reputation and reciprocity

Reputation and reciprocity are key mechanisms for cooperation in human societies, often going hand in hand to favor prosocial behavior over selfish actions. Here we review recent researches at the interface of physics and evolutionary game theory that explored these two mechanisms. We focus on image scoring as the bearer of reputation, as well as on various types of reciprocity, including direct, indirect, and network reciprocity. We review different definitions of reputation and reciprocity dynamics, and we show how these affect the evolution of cooperation in social dilemmas. We consider first-order, second-order, as well as higher-order models in well-mixed and structured populations, and we review experimental works that support and inform the results of mathematical modeling and simulations. We also provide a synthesis of the reviewed researches along with an outlook in terms of six directions that seem particularly promising to explore in the future.

Evolutionary dynamics on sequential temporal networks

Population structure is a well-known catalyst for the evolution of cooperation and has traditionally been considered to be static in the course of evolution. Conversely, real-world populations, such as microbiome communities and online social networks, frequently show a progression from tiny, active groups to huge, stable communities, which is insufficient to be captured by constant structures. Here, we propose sequential temporal networks to characterize growing networked populations, and we extend the theory of evolutionary games to these temporal networks with arbitrary structures and growth rules. We derive analytical rules under which a sequential temporal network has a higher fixation probability for cooperation than its static counterpart. Under neutral drift, the rule is simply a function of the increment of nodes and edges in each time step. But if the selection is weak, the rule is related to coalescence times on networks. In this case, we propose a mean-field approximation to calculate fixation probabilities and critical benefit-to-cost ratios with lower calculation complexity. Numerical simulations in empirical datasets also prove the cooperation-promoting effect of population growth. Our research stresses the significance of population growth in the real world and provides a high-accuracy approximation approach for analyzing the evolution in real-life systems.

Indirect reciprocity with stochastic and dual reputation updates

Cooperation is a crucial aspect of social life, yet understanding the nature of cooperation and how it can be promoted is an ongoing challenge. One mechanism for cooperation is indirect reciprocity. According to this mechanism, individuals cooperate to maintain a good reputation. This idea is embodied in a set of social norms called the "leading eight". When all information is publicly available, these norms have two major properties. Populations that employ these norms are fully cooperative, and they are stable against invasion by alternative norms. In this paper, we extend the framework of the leading eight in two directions. First, we include norms with 'dual' reputation updates. These norms do not only assign new reputations to an acting donor; they also allow to update the reputation of the passive recipient. Second, we allow social norms to be stochastic. Such norms allow individuals to evaluate others with certain probabilities. Using this framework, we characterize all evolutionarily stable norms that lead to full cooperation in the public information regime. When only the donor's reputation is updated, and all updates are deterministic, we recover the conventional model. In that case, we find two classes of stable norms: the leading eight and the 'secondary sixteen'. Stochasticity can further help to stabilize cooperation when the benefit of cooperation is comparably small. Moreover, updating the recipients' reputations can help populations to recover more quickly from errors. Overall, our study highlights a remarkable trade-off between the evolutionary stability of a norm and its robustness with respect to errors. Norms that correct errors quickly require higher benefits of cooperation to be stable.

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

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

Evolution of cooperation in multiplex networks through asymmetry between interaction and replacement

Cooperation is the foundation of society and has been the subject of numerous studies over the past three decades. However, the mechanisms underlying the spread of cooperation within a group are not yet fully comprehended. We analyze cooperation in multiplex networks, a model that has recently gained attention for successfully capturing certain aspects of human social connections. Previous studies on the evolution of cooperation in multiplex networks have shown that cooperative behavior is promoted when the two key processes in evolution, interaction and strategy replacement, are performed with the same partner as much as possible, that is, symmetrically, in a variety of network structures. We focus on a particular type of symmetry, namely, symmetry in the scope of communication, to investigate whether cooperation is promoted or hindered when interactions and strategy replacements have different scopes. Through multiagent simulations, we found some cases where asymmetry can promote cooperation, contrasting with previous studies. These results hint toward the potential effectiveness of not only symmetrical but also asymmetrical approaches in fostering cooperation within particular groups under certain social conditions.

Evolutionary stability of cooperation in indirect reciprocity under noisy and private assessment

Indirect reciprocity is a mechanism that explains large-scale cooperation in humans. In indirect reciprocity, individuals use reputations to choose whether or not to cooperate with a partner and update others' reputations. A major question is how the rules to choose their actions and the rules to update reputations evolve. In the public reputation case where all individuals share the evaluation of others, social norms called Simple Standing (SS) and Stern Judging (SJ) have been known to maintain cooperation. However, in the case of private assessment where individuals independently evaluate others, the mechanism of maintenance of cooperation is still largely unknown. This study theoretically shows for the first time that cooperation by indirect reciprocity can be evolutionarily stable under private assessment. Specifically, we find that SS can be stable, but SJ can never be. This is intuitive because SS can correct interpersonal discrepancies in reputations through its simplicity. On the other hand, SJ is too complicated to avoid an accumulation of errors, which leads to the collapse of cooperation. We conclude that moderate simplicity is a key to stable cooperation under the private assessment. Our result provides a theoretical basis for the evolution of human cooperation.

The stability of transient relationships

In contrast to long-term relationships, far less is known about the temporal evolution of transient relationships, although these constitute a substantial fraction of people's communication networks. Previous literature suggests that ratings of relationship emotional intensity decay gradually until the relationship ends. Using mobile phone data from three countries (US, UK, and Italy), we demonstrate that the volume of communication between ego and its transient alters does not display such a systematic decay, instead showing a lack of any dominant trends. This means that the communication volume of egos to groups of similar transient alters is stable. We show that alters with longer lifetimes in ego's network receive more calls, with the lifetime of the relationship being predictable from call volume within the first few weeks of first contact. This is observed across all three countries, which include samples of egos at different life stages. The relation between early call volume and lifetime is consistent with the suggestion that individuals initially engage with a new alter so as to evaluate their potential as a tie in terms of homophily.

Clustering drives cooperation on reputation networks, all else fixed

Reputation-based cooperation on social networks offers a causal mechanism between graph properties and social trust. Using a simple model, this paper demonstrates the underlying mechanism in a way that is accessible to scientists not specializing in networks or mathematics. The paper shows that when the size and degree of the network is fixed (i.e. all graphs have the same number of agents, who all have the same number of connections), it is the clustering coefficient that drives differences in how cooperative social networks are.

Random migration with tie retention promotes cooperation in the prisoner's dilemma game

Migration has the potential to induce outbreaks of cooperation, yet little is known about random migration. Does random migration really inhibit cooperation as often as previously thought? Besides, prior literature has often ignored the stickiness of social ties when designing migration protocols and assumed that players always immediately disconnect from their ex-neighbors once they migrate. However, this is not always true. Here, we propose a model where players can still retain some bonds with their ex-partners after they move from one place to another. The results show that maintaining a certain number of social ties, regardless of prosocial, exploitative, or punitive, can nevertheless facilitate cooperation even if migration occurs in a totally random fashion. Notably, it reflects that tie retention can help random migration, previously thought to be harmful to cooperation, restore the ability to spark bursts of cooperation. The maximum number of retained ex-neighbors plays an important role in facilitating cooperation. We analyze the impact of social diversity in terms of the maximum number of retained ex-neighbors and migration probability, and find that the former enhances cooperation while the latter often engenders an optimal dependence between cooperation and migration. Our results instantiate a scenario in which random migration yields the outbreak of cooperation and highlight the importance of social stickiness.

Evolutionary dynamics under partner preferences

The fact that people often have preference rankings for their partners is a distinctive aspect of human behavior. Little is known, however, about how this talent as a powerful force shapes human behavioral traits, including those which should not have been favored by selection, such as cooperation in social dilemma situations. Here we propose a dynamic model in which network-structured individuals can switch their interaction partners within neighborhoods based on their preferences. For the partner switching, we propose two interruption regimes: dictatorial regime and negotiating regime. In the dictatorial regime, focal individuals are able to suspend interactions out of preferences unilaterally. In the negotiating regime, either focal individuals or the associated partners agree to suspend, then these interactions can be successfully suspended. We investigate the evolution of cooperation under both preference-driven partner switching regimes in the context of both the weakened variant of the donation game and the standard one. Specifically, we theoretically approximate the critical conditions for cooperation to be favored by weak selection in the weakened donation game where cooperators bear a unit cost to provide a benefit for each active neighbor and simulate the evolutionary dynamics of cooperation in the standard donation game to test the robustness of the analytical results. Under dictatorial regime, selection of cooperation becomes harder when individuals have preferences for either cooperator or defector partners, implying that the expulsion of defectors by cooperators is overwhelmed by the chasing of defectors towards cooperators. Under negotiating regime, both preferences for cooperator and defector partners can significantly favor the evolution of cooperation, yet underlying mechanisms differ greatly. For preferences over cooperator partners, cooperator-cooperator interaction relationships are reinforced and the associated mutual reciprocity can resist and assimilate defectors. For preferences over defector partners, defector-defector interaction relationships are anchored, weakening defectors' exploitation over cooperators. Cooperators are thus offered much time space to interact among cospecies and spread. Our work may help better understand the critical role of preference-based adaptive partner switching in promoting the evolution of cooperation.

Mobile healthcare platforms' sustainability: The perspective of health information quality

As an emerging form of medical organization, Chinese mobile healthcare (mHealth) platforms are inherently linked to the continuous use of users, which depends on the quality of the health information provided. However, improving the health information quality of mHealth platforms is still a problem that needs to be studied and solved in order to make the platforms sustainable. Based on the reputation mechanism, this study creates a behavioral evolutionary game model for health information providers (physicians) and managers (mHealth platforms), explores the evolution process and evolutionarily stable strategy of the behaviors in various situations, and uses numerical simulation technology to analyze mHealth platforms' constraints and the influencing factors of health information quality. This study presents three key findings. First, considering reputation, health information managers and mHealth platform providers should not unilaterally optimize health information. Instead, mHealth platforms should have active quality control, and physician groups should provide high-quality health information, which is the ideal evolution of the model. Second, the rewards that physicians receive from patients and mHealth platforms for providing quality health information, the reputation benefits, the penalties that physicians suffer for providing low-quality health information, and the increased probability and cost of rent-seeking behavior that physicians may choose can effectively promote the choice of physicians to provide high-quality health information. Third, the reputation gain of mHealth platforms, the probability of mHealth platforms being exposed, and increased losses suffered from exposure can effectively promote the choice of mHealth platforms to control the quality of health information. This study can provide a theoretical basis for mHealth platforms' health information quality control, which is conducive to the healthy and sustainable development of mHealth platforms and the improvement of user satisfaction.

Social norms of fairness with reputation-based role assignment in the dictator game

A vast body of experiments share the view that social norms are major factors for the emergence of fairness in a population of individuals playing the dictator game (DG). Recently, to explore which social norms are conducive to sustaining cooperation has obtained considerable concern. However, thus, far few studies have investigated how social norms influence the evolution of fairness by means of indirect reciprocity. In this study, we propose an indirect reciprocal model of the DG and consider that an individual can be assigned as the dictator due to its good reputation. We investigate the "leading eight" norms and all second-order social norms by a two-timescale theoretical analysis. We show that when role assignment is based on reputation, four of the "leading eight" norms, including stern judging and simple standing, lead to a high level of fairness, which increases with the selection intensity. Our work also reveals that not only the correct treatment of making a fair split with good recipients but also distinguishing unjustified unfair split from justified unfair split matters in elevating the level of fairness.

Human cooperation in changing groups in a large-scale public goods game

How people cooperate to provide public goods is an important scientific question and relates to many societal problems. Previous research studied how people cooperate in stable groups in repeated or one-time-only encounters. However, most real-world public good problems occur in groups with a gradually changing composition due to old members leaving and new members arriving. How group changes are related to cooperation in public good provision is not well understood. To address this issue, we analyze a dataset from an online public goods game comprising approximately 1.5 million contribution decisions made by about 135 thousand players in about 11.3 thousand groups with about 234 thousand changes in group composition. We find that changes in group composition negatively relate to cooperation. Our results suggest that this is related to individuals contributing less in the role of newcomers than in the role of incumbents. During the process of moving from newcomer status to incumbent status, individuals cooperate more and more in line with incumbents.

The combination of social reward and punishment is conducive to the cooperation and heterogeneity of social relations

Individual behaviors and social relations influence each other. However, understanding the underlying mechanism remains challenging. From social norms controlling human behavior to individual management of interpersonal relationships, rewards and punishments are some of the most commonly used measures. Through simulating the weak prisoner's dilemma in finite populations, we find that neither a simple reward measure nor a pure punishment mechanism can extensively promote cooperation. Instead, a combination of appropriate punishment and reward mechanisms can promote cooperation's prosperity regardless of how large or small the temptation to defect is. In addition, the combination spontaneously produces inhomogeneities in social relations and individual influence, which support the continued existence of cooperative behavior. Finally, we further explain how cooperators establish a sustainable existence under the combination by investigating the social relations at different moments in a small system. These results demonstrate that dispensing rewards and punishments impartially in society is essential to social harmony.

On the evolutionary language game in structured and adaptive populations

We propose an evolutionary model for the emergence of shared linguistic convention in a population of agents whose social structure is modelled by complex networks. Through agent-based simulations, we show a process of convergence towards a common language, and explore how the topology of the underlying networks affects its dynamics. We find that small-world effects act to speed up convergence, but observe no effect of topology on the communicative efficiency of common languages. We further explore differences in agent learning, discriminating between scenarios in which new agents learn from their parents (vertical transmission) versus scenarios in which they learn from their neighbors (oblique transmission), finding that vertical transmission results in faster convergence and generally higher communicability. Optimal languages can be formed when parental learning is dominant, but a small amount of neighbor learning is included. As a last point, we illustrate an exclusion effect leading to core-periphery networks in an adaptive networks setting when agents attempt to reconnect towards better communicators in the population.

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.

Evolutionary dynamics of zero-determinant strategies in repeated multiplayer games

Several studies have confirmed the existence of zero-determinant (ZD) strategies in repeated social dilemmas since Press and Dyson's ingenious discovery of ZD strategies in iterated prisoner's dilemmas. However, less research studies evolutionary performance of multiplayer ZD strategies, especially from a theoretical perspective. Here, we use a state-clustering method to theoretically analyze evolutionary dynamics of two representative ZD strategies: generous ZD strategies and extortionate ZD strategies. We consider two new settings for multiplayer ZD strategies: competitions with all ZD strategies and competitions with all memory-one strategies, apart from the competitions between these strategies and some classical ones. Moreover, we investigate the influence of the level of generosity and extortion on evolutionary dynamics of generous and extortionate ZD strategies, which was commonly ignored in previous studies. Theoretical results show that players with limited generosity are at an advantageous place and extortioners extorting more severely hold their ground more readily. Our results may provide new insights into better understanding evolutionary dynamics of ZD strategies in repeated multiplayer games.

Reputation structure in indirect reciprocity under noisy and private assessment

Evaluation relationships are pivotal for maintaining a cooperative society. A formation of the evaluation relationships has been discussed in terms of indirect reciprocity, by modeling dynamics of good or bad reputations among individuals. Recently, a situation that individuals independently evaluate others with errors (i.e., noisy and private reputation) is considered, where the reputation structure (from what proportion of individuals in the population each receives good reputations, defined as goodness here) becomes complex, and thus has been studied mainly with numerical simulations. The present study gives a theoretical analysis of such complex reputation structure. We formulate the time change of goodness of individuals caused by updates of reputations among individuals. By considering a large population, we derive dynamics of the frequency distribution of goodnesses. An equilibrium state of the dynamics is approximated by a summation of Gaussian functions. We demonstrate that the theoretical solution well fits the numerical calculation. From the theoretical solution, we obtain a new interpretation of the complex reputation structure. This study provides a novel mathematical basis for cutting-edge studies on indirect reciprocity.

Defectors in bad circumstances possessing higher reputation can promote cooperation

In nature and human society, social relationships and behavior patterns are usually unpredictable. In any interaction, individuals will constantly have to deal with prior uncertainty. The concept of "reputation" can provide some information to mitigate such uncertainty. In previous studies, researchers have considered that only cooperators are able to maintain a high reputation; no matter the circumstances of a defector, they are classified as a faithless individual. In reality, however, some individuals will be forced to defect to protect themselves against exploitation. Therefore, it makes sense that defectors in bad circumstances could also obtain higher reputations, and cooperators can maintain higher reputations in comfortable circumstances. In this work, the reputations of individuals are calculated using the fraction of their neighbors who have the same strategy. In this way, some defectors in a population may obtain higher reputations than some cooperators. We introduce this reputation rule using heterogeneous investments in public goods games. Our numerical simulation results indicate that this reputation rule and heterogeneous investments can better stimulate cooperation. Additionally, stronger investment heterogeneity can further increase the level of cooperation. To explain this phenomenon, dynamical evolution is observed in Monte Carlo simulations. We also investigated the effects of the noise intensity of the irrational population and the original proportion of cooperation in the population. The robustness of this cooperation model was also considered with respect to the network structure and total investment, and we found that the conclusions remained the same.

Evolution of cooperation with joint liability

'Personal responsibility', one of the basic principles of social governance, requires one to be accountable for what one does. However, personal responsibility is far from the only norm ruling human interactions, especially in social and economic activities. In many collective communities such as among enterprise colleagues and family members, one's personal interests are often bound to others'-once one member breaks the rule, a group of people have to bear the punishment or sanction. Such a mechanism is termed 'joint liability'. Although many real-world cases have evidenced that joint liability can help to maintain collective collaboration, a deep and systematic theoretical analysis on how and when it promotes cooperation remains lacking. Here, we use evolutionary game theory to model an interacting system with joint liability, where one's losing credit could deteriorate the reputation of the whole group. We provide the analytical condition to predict when cooperation evolves and analytically prove that in the presence of punishment, being jointly liable greatly promotes cooperation. Our work stresses that joint liability is of great significance in promoting current economic prosperity.

Early exclusion leads to cyclical cooperation in repeated group interactions

Explaining the emergence and maintenance of cooperation among selfish individuals from an evolutionary perspective remains a grand challenge in biology, economy and social sciences. Social exclusion is believed to be an answer to this conundrum. However, previously related studies often assume one-shot interactions and ignore how free-riding is identified, which seem to be too idealistic. In this work, we consider repeated interactions where excluders need to pay a monitoring cost to identify free-riders for exclusion and free-riders cannot participate in the following possible game interactions once they are identified and excluded by excluders in the repeated interaction process. We reveal that the introduction of such exclusion can prevent the breakdown of cooperation in repeated group interactions. In particular, we demonstrate that an evolutionary oscillation among cooperators, defectors and excluders can appear in infinitely large populations when early exclusion is implemented. In addition, we find that the population spends most of the time in states where cooperators dominate for early exclusion when stochastic mutation-selection is considered in finite populations. Our results highlight that early exclusion is successful in solving the mentioned enigma of cooperation in repeated group interactions.

Network rewiring promotes cooperation in an aspirational learning model

We analyze a cooperative decision-making model that is based on individual aspiration levels using the framework of a public goods game in static and dynamic networks. Sensitivity to differences in payoff and dynamic aspiration levels modulates individual satisfaction and affects subsequent behavior. The collective outcome of such strategy changes depends on the efficiency with which aspiration levels are updated. Below a threshold learning efficiency, cooperators dominate despite short-term fluctuations in strategy fractions. Categorizing players based on their satisfaction level and the resulting strategy reveal periodic cycling between the different categories. We explain the distinct dynamics in the two phases in terms of differences in the dominant cyclic transitions between different categories of cooperators and defectors. Allowing even a small fraction of nodes to restructure their connections can promote cooperation across almost the entire range of values of learning efficiency. Our work reinforces the usefulness of an internal criterion for strategy updates, together with network restructuring, in ensuring the dominance of altruistic strategies over long time-scales.

The effects of reputation on inequality in network cooperation games

In the last several decades, ample evidence from across evolutionary biology, behavioural economics and econophysics has solidified our knowledge that reputation can promote cooperation across different contexts and environments. Higher levels of cooperation entail higher final payoffs on average, but how are these payoffs distributed among individuals? This study investigates how public and objective reputational information affects payoff inequality in repeated social dilemma interactions in large groups. I consider two aspects of inequality: excessive dispersion of final payoffs and diminished correspondence between final payoff and cooperative behaviour. I use a simple heuristics-based agent model to demonstrate that reputational information does not always increase the dispersion of final payoffs in strategically updated networks, and actually decreases it in randomly rewired networks. More importantly, reputational information almost always improves the correspondence between final payoffs and cooperative behaviour. I analyse empirical data from nine experiments of the repeated Trust, Helping, Prisoner's Dilemma and Public Good games in networks of ten or more individuals to provide partial support for the predictions. Our research suggests that reputational information not only improves cooperation but may also reduce inequality. This article is part of the theme issue 'The language of cooperation: reputation and honest signalling'.

Networks of reliable reputations and cooperation: a review

Reputation has been shown to provide an informal solution to the problem of cooperation in human societies. After reviewing models that connect reputations and cooperation, we address how reputation results from information exchange embedded in a social network that changes endogenously itself. Theoretical studies highlight that network topologies have different effects on the extent of cooperation, since they can foster or hinder the flow of reputational information. Subsequently, we review models and empirical studies that intend to grasp the coevolution of reputations, cooperation and social networks. We identify open questions in the literature concerning how networks affect the accuracy of reputations, the honesty of shared information and the spread of reputational information. Certain network topologies may facilitate biased beliefs and intergroup competition or in-group identity formation that could lead to high cooperation within but conflicts between different subgroups of a network. Our review covers theoretical, experimental and field studies across various disciplines that target these questions and could explain how the dynamics of interactions and reputations help or prevent the establishment and sustainability of cooperation in small- and large-scale societies.

This article is part of the theme issue ‘The language of cooperation: reputation and honest signalling’.

The dual problems of coordination and anti-coordination on random bipartite graphs

In some scenarios ("anti-coordination games"), individuals are better off choosing different actions than their neighbors while in other scenarios ("coordination games"), it is beneficial for individuals to choose the same strategy as their neighbors. Despite having different incentives and resulting population dynamics, it is largely unknown which collective outcome, anti-coordination or coordination, is easier to achieve. To address this issue, we focus on the distributed graph coloring problem on bipartite graphs. We show that with only two strategies, anti-coordination games (2-colorings) and coordination games (uniform colorings) are dual problems that are equally difficult to solve. To prove this, we construct an isomorphism between the Markov chains arising from the corresponding anti-coordination and coordination games under certain specific individual stochastic decision-making rules. Our results provide novel insights into solving collective action problems on networks.

No good deed goes unpunished: the social costs of prosocial behaviour

Performing costly helpful behaviours can allow individuals to improve their reputation. Those who gain a good reputation are often preferred as interaction partners and are consequently better able to access support through cooperative relationships with others. However, investing in prosocial displays can sometimes yield social costs: excessively generous individuals risk losing their good reputation, and even being vilified, ostracised or antisocially punished. As a consequence, people frequently try to downplay their prosocial actions or hide them from others. In this review, we explore when and why investments in prosocial behaviour are likely to yield social costs. We propose two key features of interactions that make it more likely that generous individuals will incur social costs when: (a) observers infer that helpful behaviour is motivated by strategic or selfish motives; and (b) observers infer that helpful behaviour is detrimental to them. We describe how the cognition required to consider ulterior motives emerges over development and how these tendencies vary across cultures - and discuss how the potential for helpful actions to result in social costs might place boundaries on prosocial behaviour as well as limiting the contexts in which it might occur. We end by outlining the key avenues and priorities for future research.

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

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

Evolutionary dynamics of higher-order interactions in social networks

We live and cooperate in networks. However, links in networks only allow for pairwise interactions, thus making the framework suitable for dyadic games, but not for games that are played in larger groups. Here, we study the evolutionary dynamics of a public goods game in social systems with higher-order interactions. First, we show that the game on uniform hypergraphs corresponds to the replicator dynamics in the well-mixed limit, providing a formal theoretical foundation to study cooperation in networked groups. Second, we unveil how the presence of hubs and the coexistence of interactions in groups of different sizes affects the evolution of cooperation. Finally, we apply the proposed framework to extract the actual dependence of the synergy factor on the size of a group from real-world collaboration data in science and technology. Our work provides a way to implement informed actions to boost cooperation in social groups.

Random choices facilitate solutions to collective network coloring problems by artificial agents

Global coordination is required to solve a wide variety of challenging collective action problems from network colorings to the tragedy of the commons. Recent empirical study shows that the presence of a few noisy autonomous agents can greatly improve collective performance of humans in solving networked color coordination games. To provide analytical insights into the role of behavioral randomness, here we study myopic artificial agents attempting to solve similar network coloring problems using decision update rules that are only based on local information but allow random choices at various stages of their heuristic reasonings. We show that the resulting efficacy of resolving color conflicts is dependent on the implementation of random behavior of agents and specific population characteristics. Our work demonstrates that distributed greedy optimization algorithms exploiting local information should be deployed in combination with occasional exploration via random choices in order to overcome local minima and achieve global coordination.

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Local information makes solving distributed network coloring problems difficult

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Greedy agents can become gridlocked, making it difficult to find a global solution

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Agents making random choices can facilitate the finding of a global coloring

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Randomness can be finely tuned to a specific underlying population structure

A game-theoretical dynamic imitation model on networks

A game-theoretical model is constructed to capture the effect of imitation on the evolution of cooperation. This imitation describes the case where successful individuals are more likely to be imitated by newcomers who will employ their strategies and social networks. Two classical repeated strategies 'always defect (ALLD)' and 'tit-for-tat (TFT)' are adopted. Mathematical analyses are mainly conducted by the method of coalescence theory. Under the assumption of a large population size and weak selection, the results show that the evolution of cooperation is promoted in this dynamic network. As we observed that the critical benefit-to-cost ratio is smaller compared to that in well-mixed populations. The critical benefit-to-cost ratio approaches a specific value which depends on three parameters, the repeated rounds of the game, the effective strategy mutation rate, and the effective link mutation rate. Specifically, for a very high value of the effective link mutation rate, the critical benefit-to-cost ratio approaches 1. Remarkably, for a low value of the effective link mutation rate, by letting the effective strategy mutation is nearly equal to zero, the critical benefit-to-cost ratio approaches [Formula: see text] for the resulting highly connected networks, which allows TFT to be evolutionary stable. It illustrates that dominance of TFTs is associated with more connected networks. This research can enrich the theory of the coevolution of game strategy and network structure with dynamic imitation.

Eco-evolutionary dynamics of cooperation in the presence of policing

Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecologically-viable free space often regulates the reproductive opportunities of the constituents. Hence, additionally, we consider the availability of free space as an ecological footprint, thus arriving at a simple eco-evolutionary model, which displays fascinating complex dynamics. As possible outcomes, we report the individual dominance of cooperators and defectors as well as a plethora of mixed states, where different strategies coexist followed by maintaining the diversity in a socio-ecological framework. These states can either be steady or oscillating, whereby oscillations are sustained by cyclic dominance among different combinations of cooperators, defectors, and punishers. We also observe a novel route to cyclic dominance where cooperators, punishers, and defectors enter a coexistence via an inverse Hopf bifurcation that is followed by an inverse period doubling route.

Chimpanzees behave prosocially in a group-specific manner

Chimpanzees act cooperatively in the wild, but whether they afford benefits to others, and whether their tendency to act prosocially varies across communities, is unclear. Here, we show that chimpanzees from neighboring communities provide valuable resources to group members at personal cost, and that the magnitude of their prosocial behavior is group specific. Provided with a resource-donation experiment allowing free (partner) choice, we observed an increase in prosocial acts across the study period in most of the chimpanzees. When group members could profit (test condition), chimpanzees provided resources more frequently and for longer durations than when their acts produced inaccessible resources (control condition). Strikingly, chimpanzees' prosocial behavior was group specific, with more socially tolerant groups acting more prosocially. We conclude that chimpanzees may purposely behave prosocially toward group members, and that the notion of group-specific sociality in nonhuman animals should crucially inform discussions on the evolution of prosocial behavior.

How strategy environment and wealth shape altruistic behaviour: cooperation rules affecting wealth distribution in dynamic networks

Societies rely on individual contributions to sustain public goods that benefit the entire community. Several mechanisms, that specify how individuals change their decisions based on past experiences, have been proposed to explain how altruists are not outcompeted by selfish counterparts. A key aspect of such strategy updates involves a comparison of an individual's latest payoff with that of a random neighbour. In reality, both the economic and social milieu often shapes cooperative behaviour. We propose a new decision heuristic, where the propensity of an individual to cooperate depends on the local strategy environment in which she is embedded as well as her wealth relative to that of her neighbours. Our decision-making model allows cooperation to be sustained and also explains the results of recent experiments on social dilemmas in dynamic networks. Final cooperation levels depend only on the extent to which the strategy environment influences altruistic behaviour but are largely unaffected by network restructuring. However, the extent of wealth inequality in the community is affected by a subtle interplay between the environmental influence on a person's decision to contribute and the likelihood of reshaping social ties, with wealth-inequality levels rising with increasing likelihood of network restructuring in some situations.

Stochastic evolutionary dynamics of trust games with asymmetric parameters

Trusting in others and reciprocating that trust with trustworthy actions are crucial to successful and prosperous societies. The trust game has been widely used to quantitatively study trust and trustworthiness, involving a sequential exchange between an investor and a trustee. Deterministic evolutionary game theory predicts no trust and no trustworthiness, whereas the behavioral experiments with the one-shot anonymous trust game show that people substantially trust and respond trustworthily. To explain these discrepancies, previous works often turn to additional mechanisms, which are borrowed from other games such as the prisoner's dilemma. Although these mechanisms lead to the evolution of trust and trustworthiness to an extent, the optimal or the most common strategy often involves no trustworthiness. In this paper, we study the impact of asymmetric demographic parameters (e.g., different population sizes) on game dynamics of the trust game. We show that, in a weak-mutation limit, stochastic evolutionary dynamics with the asymmetric parameters can lead to the evolution of high trust and high trustworthiness without any additional mechanisms in well-mixed finite populations. Even full trust and near full trustworthiness can be the most common strategies. These results are qualitatively different from those of the previous works. Our results thereby demonstrate rich evolutionary dynamics of the asymmetric trust game.