Social dilemmas among unequals

Enhancing social cohesion with cooperative bots in societies of greedy, mobile individuals

Addressing collective issues in social development requires a high level of social cohesion, characterized by cooperation and close social connections. However, social cohesion is challenged by selfish, greedy individuals. With the advancement of artificial intelligence (AI), the dynamics of human-machine hybrid interactions introduce new complexities in fostering social cohesion. This study explores the impact of simple bots on social cohesion from the perspective of human-machine hybrid populations within network. By investigating collective self-organizing movement during migration, results indicate that cooperative bots can promote cooperation, facilitate individual aggregation, and thereby enhance social cohesion. The random exploration movement of bots can break the frozen state of greedy population, help to separate defectors in cooperative clusters, and promote the establishment of cooperative clusters. However, the presence of defective bots can weaken social cohesion, underscoring the importance of carefully designing bot behavior. Our research reveals the potential of bots in guiding social self-organization and provides insights for enhancing social cohesion in the era of human-machine interaction within social networks.

Efficiency and resilience of cooperation in asymmetric social dilemmas

Direct reciprocity is a powerful mechanism for cooperation in social dilemmas. The very logic of reciprocity, however, seems to require that individuals are symmetric, and that everyone has the same means to influence each others' payoffs. Yet in many applications, individuals are asymmetric. Herein, we study the effect of asymmetry in linear public good games. Individuals may differ in their endowments (their ability to contribute to a public good) and in their productivities (how effective their contributions are). Given the individuals' productivities, we ask which allocation of endowments is optimal for cooperation. To this end, we consider two notions of optimality. The first notion focuses on the resilience of cooperation. The respective endowment distribution ensures that full cooperation is feasible even under the most adverse conditions. The second notion focuses on efficiency. The corresponding endowment distribution maximizes group welfare. Using analytical methods, we fully characterize these two endowment distributions. This analysis reveals that both optimality notions favor some endowment inequality: More productive players ought to get higher endowments. Yet the two notions disagree on how unequal endowments are supposed to be. A focus on resilience results in less inequality. With additional simulations, we show that the optimal endowment allocation needs to account for both the resilience and the efficiency of cooperation.

Cooperation among unequal players with aspiration-driven learning

Direct reciprocity promotes the evolution of cooperation when players are sufficiently equal, such that they have similar influence on each other. In the light of ubiquitous inequality, this raises the question of how reciprocity evolves among unequal players. Existing studies on inequality mainly focus on payoff-driven learning rules, which rely on the knowledge of others' strategies. However, inferring one's strategy is a difficult task even if the whole interaction history is known. Here, we consider aspiration-driven learning rules, where players seek strategies that satisfy their aspirations based on their own information. Under aspiration-driven learning rules, we explore the evolutionary dynamics among players with inequality in endowments and productivity. We model the interactions among unequal players with asymmetric games and characterize the condition where cooperation is feasible. Remarkably, we find that aspiration-driven learning rules lead to a higher level of cooperation than payoff-driven ones over a wide range of inequality. Moreover, our results show that high aspiration levels are conducive to the evolution of cooperation when more productive players are equipped with higher endowments. Our work highlights the advantages of aspiration-driven learning for promoting cooperation among unequal players and suggests that aspiration-based decision-making may be more beneficial for the collective.

Complex pathways to cooperation emergent from asymmetry in heterogeneous populations

Cooperation within asymmetric populations has garnered significant attention in evolutionary games. This paper explores cooperation evolution in populations with weak and strong players, using a game model where players choose between cooperation and defection. Asymmetry stems from different benefits for strong and weak cooperators, with their benefit ratio indicating the degree of asymmetry. Varied rankings of parameters including the asymmetry degree, cooperation costs, and benefits brought by weak players give rise to scenarios including the prisoner's dilemma (PDG) for both player types, the snowdrift game (SDG), and mixed PDG-SDG interactions. Our results indicate that in an infinite well-mixed population, defection remains the dominant strategy when strong players engage in the prisoner's dilemma game. However, if strong players play snowdrift games, global cooperation increases with the proportion of strong players. In this scenario, strong cooperators can prevail over strong defectors when the proportion of strong players is low, but the prevalence of cooperation among strong players decreases as their proportion increases. In contrast, within a square lattice, the optimum global cooperation emerges at intermediate proportions of strong players with moderate degrees of asymmetry. Additionally, weak players protect cooperative clusters from exploitation by strong defectors. This study highlights the complex dynamics of cooperation in asymmetric interactions, contributing to the theory of cooperation in asymmetric games.

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

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

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

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

Partner choice and cooperation in social dilemmas can increase resource inequality

Cooperation is more likely when individuals can choose their interaction partner. However, partner choice may be detrimental in unequal societies, in which individuals differ in available resources and productivity, and thus in their attractiveness as interaction partners. Here we experimentally examine this conjecture in a repeated public goods game. Individuals (n = 336), participating in groups of eight participants, are assigned a high or low endowment and a high or low productivity factor (the value that their cooperation generates), creating four unique participant types. On each round, individuals are either assigned a partner (assigned partner condition) or paired based on their self-indicated preference for a partner type (partner choice condition). Results show that under partner choice, individuals who were assigned a high endowment and high productivity almost exclusively interact with each other, forcing other individuals into less valuable pairs. Consequently, pre-existing resource differences between individuals increase. These findings show how partner choice in social dilemmas can amplify resource inequality.

The effect of environmental information on evolution of cooperation in stochastic games

Many human interactions feature the characteristics of social dilemmas where individual actions have consequences for the group and the environment. The feedback between behavior and environment can be studied with the framework of stochastic games. In stochastic games, the state of the environment can change, depending on the choices made by group members. Past work suggests that such feedback can reinforce cooperative behaviors. In particular, cooperation can evolve in stochastic games even if it is infeasible in each separate repeated game. In stochastic games, participants have an interest in conditioning their strategies on the state of the environment. Yet in many applications, precise information about the state could be scarce. Here, we study how the availability of information (or lack thereof) shapes evolution of cooperation. Already for simple examples of two state games we find surprising effects. In some cases, cooperation is only possible if there is precise information about the state of the environment. In other cases, cooperation is most abundant when there is no information about the state of the environment. We systematically analyze all stochastic games of a given complexity class, to determine when receiving information about the environment is better, neutral, or worse for evolution of cooperation.

Personal sustained cooperation based on networked evolutionary game theory

Evolutionary game theory on complex networks provides an effective theoretical tool to explain the emergence of sustained cooperative behavior. Human society has formed various organizational networks. The network structure and individual behavior take on a variety of forms. This diversity provides the basis for choice, so it is crucial for the emergence of cooperation. This article provides a dynamic algorithm for individual network evolution, and calculates the importance of different nodes in the network evolution process. In the dynamic evolution simulation, the probability of the cooperation strategy and betrayal strategy is described. In the individual interaction network, cooperative behavior will promote the continuous evolution of individual relationships and form a better aggregative interpersonal network. The interpersonal network of betrayal has been in a relatively loose state, and its continuity must rely on the participation of new nodes, but there will be certain "weak links" in the existing nodes of the network.

Zealous cooperation does not always promote cooperation in public goods games

There is a conventional belief that prosocial behaviors cannot arise through selfish human nature, because defection always exploits cooperation to achieve a higher payoff at an individual level. Unyieldingly, some people hope to move society to cooperation through their zealous cooperation, regardless of payoffs. From the perspective of spatial evolutionary games, however, such zealous behavior is unnecessary because cooperation can emerge from selfish human nature by aggregating in evolution. Yet, to what extent can zealous cooperation induce others to cooperate? We assume a fraction of zealous agents in spatial public goods games who always cooperate. The results show that a moderate proportion of these zealous cooperators can diminish the cooperation level in the system, and cooperation is only promoted when zealots are many. Regarding spatial behaviors, the areas of zealous cooperation in a medium density can prevent evolutionary cooperation from passing through and aggregating. The phenomenon of zealous cooperation impeding cooperation becomes more pronounced when agents become less random and more selfish. This is because dotted zealous cooperation provides significant payoffs to neighboring defection, making them more solid in fitness. In this way, we also find that when zealous cooperators have low productivity, the neighbors receive fewer benefits by exploitation, thus allowing cooperation to spread. We also study replicator dynamics in unstructured populations where zealous cooperation always promotes cooperation, agreeing that zealous cooperation hindering cooperation is a spatial effect.

Cooperation and coordination in heterogeneous populations

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

Complex evolutionary interactions in multiple populations

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

Evolution of cooperation under a generalized death-birth process

According to the evolutionary death-birth protocol, a player is chosen randomly to die and neighbors compete for the available position proportional to their fitness. Hence, the status of the focal player is completely ignored and has no impact on the strategy update. In this paper, we revisit and generalize this rule by introducing a weight factor to compare the payoff values of the focal and invading neighbors. By means of evolutionary graph theory, we analyze the model on joint transitive graphs to explore the possible consequences of the presence of a weight factor. We find that focal weight always hinders cooperation under weak selection strength. Surprisingly, the results show a nontrivial tipping point of the weight factor where the threshold of cooperation success shifts from positive to negative infinity. Once focal weight exceeds this tipping point, cooperation becomes unreachable. Our theoretical predictions are confirmed by Monte Carlo simulations on a square lattice of different sizes. We also verify the robustness of the conclusions to arbitrary two-player prisoner's dilemmas, to dispersal graphs with arbitrary edge weights, and to interaction and dispersal graphs overlapping arbitrarily.

Diversity enables the jump towards cooperation for the Traveler's Dilemma

Social dilemmas are situations in which collective welfare is at odds with individual gain. One widely studied example, due to the conflict it poses between human behaviour and game theoretic reasoning, is the Traveler's Dilemma. The dilemma relies on the players' incentive to undercut their opponent at the expense of losing a collective high payoff. Such individual incentive leads players to a systematic mutual undercutting until the lowest possible payoff is reached, which is the game's unique Nash equilibrium. However, if players were satisfied with a high payoff -that is not necessarily higher than their opponent's- they would both be better off individually and collectively. Here, we explain how it is possible to converge to this cooperative high payoff equilibrium. Our analysis focuses on decomposing the dilemma into a local and a global game. We show that players need to escape the local maximisation and jump to the global game, in order to reach the cooperative equilibrium. Using a dynamic approach, based on evolutionary game theory and learning theory models, we find that diversity, understood as the presence of suboptimal strategies, is the general mechanism that enables the jump towards cooperation.

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.

Resource asymmetry reduces generosity and paying forward generosity, among the resource-advantaged and disadvantaged

Decisions to benefit others often entail generalized reciprocity: helping someone who cannot directly return benefits in the future; instead, the beneficiary may "pay it forward" to someone else. While much past work demonstrates that people pay forward generosity, experimental tests of these processes typically assume that people have equal access to same-valued resources that they can use to benefit others. Yet this is rare in daily life, where people commonly experience asymmetries in the resources that they have to help others and to pay forward help received. In an experiment, we find that acts of generalized reciprocity-including initiating generosity and, upon being treated generously, paying it forward-are reduced when there is resource asymmetry between potential benefactors. Results show that the detriments of resource asymmetry occur among both the resource-advantaged and the disadvantaged. Asymmetry in available resources, and inequality more broadly, is thus critical for understanding patterns of generosity.

From asymmetric to symmetric consumption opportunities: Extractions from common resources by privileged and underprivileged group members

In social dilemmas, asymmetric opportunities among actors can aggravate the conflict between individual and collective interests. We examine if and under what conditions redistributing extraction opportunities symmetrically fosters sustainable resource consumption. Participants in two studies (total n=640) completed a common resource game, first under asymmetric distribution of extraction opportunities (i.e., two advantaged group members could extract more than two disadvantaged group members) and then under symmetric distribution (i.e., all group members could extract the same amount). Advantaged (vs. disadvantaged) individuals took more from the resource in the asymmetric game and voted more often for the maintenance of the asymmetric system. Consumption was overall not more sustainable under symmetric (vs. asymmetric) distribution. We did not find evidence that these effects depend on the legitimacy of status positions. Of note, the symmetric game elicited higher satisfaction and fairness ratings in both status groups. The findings demonstrate how unequal access to resources fosters unequal consumption despite broad support for symmetry as the fairer system.

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.

Evolutionary instability of selfish learning in repeated games

Across many domains of interaction, both natural and artificial, individuals use past experience to shape future behaviors. The results of such learning processes depend on what individuals wish to maximize. A natural objective is one's own success. However, when two such "selfish" learners interact with each other, the outcome can be detrimental to both, especially when there are conflicts of interest. Here, we explore how a learner can align incentives with a selfish opponent. Moreover, we consider the dynamics that arise when learning rules themselves are subject to evolutionary pressure. By combining extensive simulations and analytical techniques, we demonstrate that selfish learning is unstable in most classical two-player repeated games. If evolution operates on the level of long-run payoffs, selection instead favors learning rules that incorporate social (other-regarding) preferences. To further corroborate these results, we analyze data from a repeated prisoner's dilemma experiment. We find that selfish learning is insufficient to explain human behavior when there is a trade-off between payoff maximization and fairness.

Direct reciprocity between individuals that use different strategy spaces

In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate.

Direct reciprocity can lead to cooperation between individuals who meet in repeated encounters. The shadow of the future casts an incentive to cooperate. If I cooperate today, you may cooperate tomorrow. But if I defect today, you may defect tomorrow. In most studies of direct reciprocity it is assumed that both players explore the same space of possible strategies. In contrast, here we study interactions between players that use different strategy spaces and therefore utilize different memory capacities. Surprisingly, we find that more complex strategy spaces often lose out against simpler ones. The social optimum, however, is achieved if all players use the more complex space. Therefore, the game between strategy spaces becomes a higher order social dilemma.

The ecology of wealth inequality in animal societies

Individuals vary in their access to resources, social connections and phenotypic traits, and a central goal of evolutionary biology is to understand how this variation arises and influences fitness. Parallel research on humans has focused on the causes and consequences of variation in material possessions, opportunity and health. Central to both fields of study is that unequal distribution of wealth is an important component of social structure that drives variation in relevant outcomes. Here, we advance a research framework and agenda for studying wealth inequality within an ecological and evolutionary context. This ecology of inequality approach presents the opportunity to reintegrate key evolutionary concepts as different dimensions of the link between wealth and fitness by (i) developing measures of wealth and inequality as taxonomically broad features of societies, (ii) considering how feedback loops link inequality to individual and societal outcomes, (iii) exploring the ecological and evolutionary underpinnings of what makes some societies more unequal than others, and (iv) studying the long-term dynamics of inequality as a central component of social evolution. We hope that this framework will facilitate a cohesive understanding of inequality as a widespread biological phenomenon and clarify the role of social systems as central to evolutionary biology.

Inequality and cooperation in social networks

Social networks are fundamental to the broad scale cooperation observed in human populations. But by structuring the flow of benefits from cooperation, networks also create and sustain macro-level inequalities. Here we ask how two aspects of inequality shape the evolution of cooperation in dynamic social networks. Results from a crowdsourced experiment (N = 1080) show that inequality alters the distribution of cooperation within networks such that participants engage in more costly cooperation with their wealthier partners in order to maintain more valuable connections to them. Inequality also influences network dynamics, increasing the tendency for participants to seek wealthier partners, resulting in structural network change. These processes aggregate to alter network structures and produce greater system-level inequality. The findings thus shed critical light on how networks serve as both boon and barrier to macro-level human flourishing.

Dynamical robustness of complex networks subject to long-range connectivity

In spite of a few attempts in understanding the dynamical robustness of complex networks, this extremely important subject of research is still in its dawn as compared to the other dynamical processes on networks. We hereby consider the concept of long-range interactions among the dynamical units of complex networks and demonstrate for the first time that such a characteristic can have noteworthy impacts on the dynamical robustness of networked systems, regardless of the underlying network topology. We present a comprehensive analysis of this phenomenon on top of diverse network architectures. Such dynamical damages being able to substantially affect the network performance, determining mechanisms that boost the robustness of networks becomes a fundamental question. In this work, we put forward a prescription based upon self-feedback that can efficiently resurrect global rhythmicity of complex networks composed of active and inactive dynamical units, and thus can enhance the network robustness. We have been able to delineate the whole proposition analytically while dealing with all d -path adjacency matrices, having an excellent agreement with the numerical results. For the numerical computations, we examine scale-free networks, Watts–Strogatz small-world model and also Erdös–Rényi random network, along with Landau–Stuart oscillators for casting the local dynamics.

Willingness to produce disadvantageous outcomes in cooperative tasks is modulated by recent experience

Cooperative behavior represents a situation in which individuals sometimes act in a way that produces a gain to another at a cost to themselves. This may be explained by a history of repeated interactions with others in which such behavior has resulted in reciprocal cooperation from others. Sometimes, even with reciprocal cooperation, gains and costs are unbalanced between partners. In this case, there is evidence that people may present an aversion to both disadvantageous and advantageous distributions of gains. In other words, they may act in such a way as to ensure an equal outcome among all group members. Aversion to inequity that benefits oneself (advantageous inequity (AI) aversion) may be more dependent on social and cultural cues than aversion to inequity that benefits others (disadvantageous inequity (DI) aversion). Using both between-subjects (Experiment 1) and within-subjects (Experiment 2) manipulations, the influence of recent experience with AI on participants' willingness to produce DI was explored within the context of a two-player card game. In initial game phases, the percentage of trials in which the participant experienced AI was manipulated. In subsequent game phases, participants had the opportunity to produce DI to themselves. The results from both experiments suggest that aversion to DI is reduced by recent experience with AI. This procedure allows social influences on DI to be tested, which may be important for providing a psychological explanation of cultural differences in aversion to DI.

The Link Between Income, Income Inequality, and Prosocial Behavior Around the World

Abstract. The questions of whether high-income individuals are more prosocial than low-income individuals and whether income inequality moderates this effect have received extensive attention. We shed new light on this topic by analyzing a large-scale dataset with a representative sample of respondents from 133 countries ( N = 948,837). We conduct a multiverse analysis with 30 statistical models: 15 models predicting the likelihood of donating money to charity and 15 models predicting the likelihood of volunteering time to an organization. Across all model specifications, high-income individuals were more likely to donate their money and volunteer their time than low-income individuals. High-income individuals were more likely to engage in prosocial behavior under high (vs. low) income inequality. Avenues for future research and potential mechanisms are discussed.

A unified framework of direct and indirect reciprocity

Direct and indirect reciprocity are key mechanisms for the evolution of cooperation. Direct reciprocity means that individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means that they also consider the experiences of others. Although these two mechanisms are intertwined, they are typically studied in isolation. Here, we introduce a mathematical framework that allows us to explore both kinds of reciprocity simultaneously. We show that the well-known 'generous tit-for-tat' strategy of direct reciprocity has a natural analogue in indirect reciprocity, which we call 'generous scoring'. Using an equilibrium analysis, we characterize under which conditions either of the two strategies can maintain cooperation. With simulations, we additionally explore which kind of reciprocity evolves when members of a population engage in social learning to adapt to their environment. Our results draw unexpected connections between direct and indirect reciprocity while highlighting important differences regarding their evolvability.

Modeling pluralism and self-regulation explains the emergence of cooperation in networked societies

Understanding the dynamics of cooperative behavior of individuals in complex societies represents a fundamental research question which puzzles scientists working in heterogeneous fields. Many studies have been developed using the unitary agent assumption, which embeds the idea that when making decisions, individuals share the same socio-cultural parameters. In this paper, we propose the ECHO-EGN model, based on Evolutionary Game Theory, which relaxes this strong assumption by considering the heterogeneity of three fundamental socio-cultural aspects ruling the behavior of groups of people: the propensity to be more cooperative with members of the same group (Endogamic cooperation), the propensity to cooperate with the public domain (Civicness) and the propensity to prefer connections with members of the same group (Homophily). The ECHO-EGN model is shown to have high performance in describing real world behavior of interacting individuals living in complex environments. Extensive numerical experiments allowing the comparison of real data and model simulations confirmed that the introduction of the above mechanisms enhances the realism in the modelling of cooperation dynamics. Additionally, theoretical findings allow us to conclude that endogamic cooperation may limit significantly the emergence of cooperation.

Prosociality from the perspective of environmental psychology

Pro-environmental behavior, a form of prosocial behavior that ultimately benefits all humanity, is essential for addressing climate change. This review presents pro-environmental behavior in a social dilemma framework describing how non-aligned interests in nested groups (e.g. smaller groups with interests opposing the interests of a superordinate group entailing the smaller groups) and unequal opportunities (e.g. differential access to resources) constitute barriers to pro-environmental behavior. We then summarize recent literature on three ways in which these barriers could be addressed. Specifically, we review how individual and conflicting interests might be overcome and benefits for the collective can be achieved by (1) collective action and global identities, (2) applying insights from another global crisis, the COVID-19 pandemic, and (3) a shift to research methods that consider the nested structure of and unequal opportunities within global crises as well as high-impact actions. Taken together, these approaches might foster one form of prosociality, pro-environmental behavior, that is desperately needed in the pursuit of sustainability.

(Mis)perceiving cooperativeness

Cooperation is crucial for the success of social interactions. Given its importance, humans should readily be able to use available cues to predict how likely others are to cooperate. Here, we review the empirical literature on how accurate such predictions are. To this end, we distinguish between three classes of cues: behavioral (including past decisions), personal (including gender, attractiveness, and group membership) and situational (including the benefits to cooperation and the ability to communicate with each other). We discuss (i) how each cue correlates with future cooperative decisions and (ii) whether people correctly anticipate each cue's predictive value. We find that people are fairly accurate in interpreting behavioral and situational cues. However, they often misperceive the value of personal cues.

Reciprocity With Unequal Payoffs: Cooperative and Uncooperative Interactions Affect Disadvantageous Inequity Aversion

Cooperation among unrelated individuals can evolve through reciprocity. Reciprocal cooperation is the process in which lasting social interactions provide the opportunity to learn about others' behavior, and to further predict the outcome of future encounters. Lasting social interactions may also decrease aversion to unequal distribution of gains – when individuals accept inequity payoffs knowing about the possibility of future encounters. Thus, reciprocal cooperation and aversion to inequity can be complementary phenomena. The present study investigated the effects of cooperative and uncooperative interactions on participants' aversion to disadvantageous inequity. Participants played an experimental task in the presence of a confederate who acted as a second participant. In reality, the participant interacted with a computer programed to make cooperative and uncooperative choices. After interacting with a cooperative or uncooperative computer, participants chose between blue cards to produce larger gains to the computer and smaller for him/her or green cards to produce equal and smaller gains for both. Results confirmed our first hypothesis that uncooperative interactions would produce aversion to disadvantageous inequity. Lastly, half of the participants were informed that points received during the experiment could be later exchanged for money, and half were not. Results indicated that information about monetary outcomes did not affect aversion to inequity, contradicting our second hypothesis. We discuss these results in the light of theories of reciprocal cooperation, inequity aversion, and conformity.

Avoiding the bullies: The resilience of cooperation among unequals

Can egalitarian norms or conventions survive the presence of dominant individuals who are ensured of victory in conflicts? We investigate the interaction of power asymmetry and partner choice in games of conflict over a contested resource. Previous models of cooperation do not include both power inequality and partner choice. Furthermore, models that do include power inequalities assume a static game where a bully's advantage does not change. They have therefore not attempted to model complex and realistic properties of social interaction. Here, we introduce three models to study the emergence and resilience of cooperation among unequals when interaction is random, when individuals can choose their partners, and where power asymmetries dynamically depend on accumulated payoffs. We find that the ability to avoid bullies with higher competitive ability afforded by partner choice mostly restores cooperative conventions and that the competitive hierarchy never forms. Partner choice counteracts the hyper dominance of bullies who are isolated in the network and eliminates the need for others to coordinate in a coalition. When competitive ability dynamically depends on cumulative payoffs, complex cycles of coupled network-strategy-rank changes emerge. Effective collaborators gain popularity (and thus power), adopt aggressive behavior, get isolated, and ultimately lose power. Neither the network nor behavior converge to a stable equilibrium. Despite the instability of power dynamics, the cooperative convention in the population remains stable overall and long-term inequality is completely eliminated. The interaction between partner choice and dynamic power asymmetry is crucial for these results: without partner choice, bullies cannot be isolated, and without dynamic power asymmetry, bullies do not lose their power even when isolated. We analytically identify a single critical point that marks a phase transition in all three iterations of our models. This critical point is where the first individual breaks from the convention and cycles start to emerge.

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.

The dynamics of injunctive social norms

Injunctive social norms are behaviours that one is expected to follow and expects others to follow in a given social situation; they are maintained by the threat of disapproval or punishment and by the process of internalization. Injunctive norms govern all aspects of our social life but the understanding of their effects on individual and group behaviour is currently rather incomplete. Here I develop a general mathematical approach describing the dynamics of injunctive norms in heterogeneous groups. My approach captures various costs and benefits, both material and normative, associated with norm-related behaviours including punishment and disapproval by others. It also allows for errors in decision-making and explicitly accounts for differences between individuals in their values, beliefs about the population state, and sensitivity to the actions of others. In addition, it enables one to study the consequences of mixing populations with different normative values and the effects of persuasive interventions. I describe how interactions of these factors affect individual and group behaviour. As an illustration, I consider policies developed by practitioners to abolish the norms of footbinding and female genital cutting, to decrease college students' drinking, and to increase pro-environmental behaviours. The theory developed here can be used for achieving a better understanding of historical and current social processes as well as for developing practical policies better accounting for human social behaviour.

Self-reliance crowds out group cooperation and increases wealth inequality

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

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

Heterogeneous groups cooperate in public good problems despite normative disagreements about individual contribution levels

Norms can promote human cooperation to provide public goods. Yet, the potential of norms to promote cooperation may be limited to homogeneous groups in which all members benefit equally from the public good. Individual heterogeneity in the benefits of public good provision is commonly conjectured to bring about normative disagreements that harm cooperation. However, the role of these normative disagreements remains unclear because they are rarely directly measured or manipulated. In a laboratory experiment, we first measure participants' views on the appropriate way to contribute to a public good with heterogeneous returns. We then use this information to sort people into groups that either agree or disagree on these views, thereby manipulating group-level disagreement on normative views. Participants subsequently make several incentivized contribution decisions in a public goods game with peer punishment. We find that although there are considerable disagreements about individual contribution levels in heterogeneous groups, these disagreements do not impede cooperation. While cooperation is maintained because low contributors are punished, participants do not use punishment to impose their normative views on others. The contribution levels at which groups cooperate strongly relate to the average normative views of these groups.

Experimental Games and Social Decision Making

Experimental games model situations in which the future outcomes of individuals and groups depend on their own choices and on those of other (groups of) individuals. Games are a powerful tool to identify the neural and psychological mechanisms underlying interpersonal and group cooperation and coordination. Here we discuss recent developments in how experimental games are used and adapted, with an increased focus on repeated interactions, partner control through sanctioning, and partner (de)selection for future interactions. Important advances have been made in uncovering the neurobiological underpinnings of key factors involved in cooperation and coordination, including social preferences, cooperative beliefs, (emotion) signaling, and, in particular, reputations and (in)direct reciprocity. Emerging trends at the cross-sections of psychology, economics, and the neurosciences include an increased focus on group heterogeneities, intergroup polarization and conflict, cross-cultural differences in cooperation and norm enforcement, and neurocomputational modeling of the formation and updating of social preferences and beliefs.

Evolving cooperation in multichannel games

Humans routinely engage in many distinct interactions in parallel. Team members collaborate on several concurrent projects, and even whole nations interact with each other across a variety of issues, including trade, climate change and security. Yet the existing theory of direct reciprocity studies isolated repeated games. Such models cannot account for strategic attempts to use the vested interests in one game as a leverage to enforce cooperation in another. Here we introduce a general framework of multichannel games. Individuals interact with each other over multiple channels; each channel is a repeated game. Strategic choices in one channel can affect decisions in another. With analytical equilibrium calculations for the donation game and evolutionary simulations for several other games we show that such linkage facilitates cooperation. Our results suggest that previous studies tend to underestimate the human potential for reciprocity. When several interactions occur in parallel, people often learn to coordinate their behavior across games to maximize cooperation in each of them.

Freedom of choice adds value to public goods

Public goods, ranging from judiciary to sanitation to parkland, permeate daily life. They have been a subject of intense interdisciplinary study, with a traditional focus being on participation levels in isolated public goods games (PGGs) as opposed to a more recent focus on participation in PGGs embedded into complex social networks. We merged the two perspectives by arranging voluntary participants into one of three network configurations, upon which volunteers played a number of iterated PGGs within their network neighborhood. The purpose was to test whether the topology of social networks or a freedom to express preferences for some local public goods over others affect participation. The results show that changes in social networks are of little consequence, yet volunteers significantly increase participation when they freely express preferences. Surprisingly, the increase in participation happens from the very beginning of the game experiment, before any information about how others play can be gathered. Such information does get used later in the game as volunteers seek to correlate contributions with higher returns, thus adding significant value to public goods overall. These results are ascribable to a small number of behavioral phenotypes, and suggest that societies may be better off with bottom-up schemes for public goods provision.

Collective choice fosters sustainable resource management in the presence of asymmetric opportunities

Asymmetric distribution of opportunities among actors can reinforce the conflict between individual and collective interests in social dilemma situations. The present study investigates the interplay of asymmetric distribution of opportunities to consume resources and three choice systems: individual choice, median choice, and majority voting. Participants (N = 248) took part in a common resource game in groups of four under each of the three choice systems. We examined the average percentage taken of the resource as well as satisfaction and fairness ratings depending on the choice system in interaction with (a) whether the distribution of opportunities among group members was symmetric versus asymmetric, and (b) the status of an actor (advantaged versus disadvantaged) within asymmetric groups. Both implemented collective choice systems (median choice and majority voting) increased sustainable resource management, especially in asymmetric groups, by restricting overconsumption of advantaged individuals, as well as satisfaction and fairness ratings. Collective choice increased collective welfare by increasing profits of disadvantaged individuals and members of symmetric groups. The results indicate that in the presence of asymmetric distribution of opportunities, collective choice is a means to reconcile the conflict between individual and collective interests in social dilemmas and to foster sustainable resource management.

Punishing the privileged: Selfish offers from high-status allocators elicit greater punishment from third-party arbitrators

Individuals high in socioeconomic status (SES) are often viewed as valuable members of society. However, the appeal of high-SES people exists in tension with our aversion to inequity. Little experimental work has directly examined how people rectify inequitable distributions between two individuals varying in SES. The objective of the present study was to examine how disinterested third parties adjudicate inequity in the context of concrete financial allocations between a selfish allocator and a recipient who was the victim of the allocator’s selfish offer. Specifically, this study focused on whether knowing the SES of the victim or the allocator affected the participant’s decisions to punish the selfish allocator. In two experiments (N = 999), participants completed a modified third-party Ultimatum Game in which they arbitrated inequitable exchanges between an allocator and a recipient. Although participants generally preferred to redistribute inequitable exchanges without punishing players who made unfair allocations, we observed an increased preference for punitive solutions as offers became increasingly selfish. This tendency was especially pronounced when the victim was low in SES or when the perpetrator was high in SES, suggesting a tendency to favor the disadvantaged even among participants reporting high subjective SES. Finally, punitive responses were especially likely when the context emphasized the allocator’s privileged status rather than the recipient’s underprivileged status. These findings inform our understanding of how SES biases retributive justice even in non-judicial contexts that minimize the salience of punishment.

PRISM-games 3.0: Stochastic Game Verification with Concurrency, Equilibria and Time

We present a major new release of the PRISM-games model checker, featuring multiple significant advances in its support for verification and strategy synthesis of stochastic games. Firstly, concurrent stochastic games bring more realistic modelling of agents interacting in a concurrent fashion. Secondly, equilibria-based properties provide a means to analyse games in which competing or collaborating players are driven by distinct objectives. Thirdly, a real-time extension of (turn-based) stochastic games facilitates verification and strategy synthesis for systems where timing is a crucial aspect. This paper describes the advances made in the tool’s modelling language, property specification language and model checking engines in order to implement this new functionality. We also summarise the performance and scalability of the tool, and describe a selection of case studies, ranging from security protocols to robot coordination, which highlight the benefits of the new features.