A unified framework of direct and indirect reciprocity

Computational evolution of social norms in well-mixed and group-structured populations

Models of indirect reciprocity study how social norms promote cooperation. In these models, cooperative individuals build up a positive reputation, which in turn helps them in their future interactions. The exact reputational benefits of cooperation depend on the norm in place, which may change over time. Previous research focused on the stability of social norms. Much less is known about how social norms initially evolve when competing with many others. A comprehensive evolutionary analysis, however, has been difficult. Even among the comparably simple space of so-called third-order norms, there are thousands of possibilities, each one inducing its own reputation dynamics. To address this challenge, we use large-scale computer simulations. We study the reputation dynamics of each third-order norm and all evolutionary transitions between them. In contrast to established work with only a handful of norms, we find that cooperation is hard to maintain in well-mixed populations. However, within group-structured populations, cooperation can emerge. The most successful norm in our simulations is particularly simple. It regards cooperation as universally positive, and defection as usually negative-unless defection takes the form of justified punishment. This research sheds light on the complex interplay of social norms, their induced reputation dynamics, and population structure.

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.

Evolution of reciprocity with limited payoff memory

Direct reciprocity is a mechanism for the evolution of cooperation in repeated social interactions. According to the literature, individuals naturally learn to adopt conditionally cooperative strategies if they have multiple encounters with their partner. Corresponding models have greatly facilitated our understanding of cooperation, yet they often make strong assumptions on how individuals remember and process payoff information. For example, when strategies are updated through social learning, it is commonly assumed that individuals compare their average payoffs. This would require them to compute (or remember) their payoffs against everyone else in the population. To understand how more realistic constraints influence direct reciprocity, we consider the evolution of conditional behaviours when individuals learn based on more recent experiences. Even in the most extreme case that they only take into account their very last interaction, we find that cooperation can still evolve. However, such individuals adopt less generous strategies, and they cooperate less often than in the classical setup with average payoffs. Interestingly, once individuals remember the payoffs of two or three recent interactions, cooperation rates quickly approach the classical limit. These findings contribute to a literature that explores which kind of cognitive capabilities are required for reciprocal cooperation. While our results suggest that some rudimentary form of payoff memory is necessary, it suffices to remember a few interactions.

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.

When do stereotypes undermine indirect reciprocity?

Social reputations provide a powerful mechanism to stimulate human cooperation, but observing individual reputations can be cognitively costly. To ease this burden, people may rely on proxies such as stereotypes, or generalized reputations assigned to groups. Such stereotypes are less accurate than individual reputations, and so they could disrupt the positive feedback between altruistic behavior and social standing, undermining cooperation. How do stereotypes impact cooperation by indirect reciprocity? We develop a theoretical model of group-structured populations in which individuals are assigned either individual reputations based on their own actions or stereotyped reputations based on their groups' behavior. We find that using stereotypes can produce either more or less cooperation than using individual reputations, depending on how widely reputations are shared. Deleterious outcomes can arise when individuals adapt their propensity to stereotype. Stereotyping behavior can spread and can be difficult to displace, even when it compromises collective cooperation and even though it makes a population vulnerable to invasion by defectors. We discuss the implications of our results for the prevalence of stereotyping and for reputation-based cooperation in structured populations.

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.

Adaptations to infer fitness interdependence promote the evolution of cooperation

The evolution of cooperation is a major question in the biological and behavioral sciences. While most theoretical studies model cooperation in the context of an isolated interaction (e.g., a Prisoner's Dilemma), humans live in heterogeneous social environments, characterized by large variations in fitness interdependence-the extent to which one's fitness is affected by others. Theoretical and experimental work indicates that humans can infer, and respond to, variations in interdependence. In a heterogeneous ancestral environment, these psychological mechanisms to infer fitness interdependence could have provided a selective advantage, allowing individuals to maximize their fitness by deciding when and with whom to cooperate. Yet, to date, the link between cognitive inference, variation in fitness interdependence, and cooperation remains unclear. Here we introduce a theoretical framework to study the evolution of inference and cooperation in heterogeneous social environments, where individuals experience interactions with varying levels of corresponding interests. Using a combination of evolutionary game theory and agent-based modeling, we model the evolution of adaptive agents, who incur a cost to infer interdependence, in populations of fixed-behavior agents who always cooperate or defect. Our results indicate that natural selection could promote the evolution of psychological mechanisms to infer fitness interdependence, provided that there is enough variation in fitness interdependence to offset the cost of inference. Under certain conditions, the fixation of adaptive agents results in higher levels of cooperation. This depends crucially on the type of inference performed and the features of the interdependence landscape.

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.

Reconstructing signed relations from interaction data

Positive and negative relations play an essential role in human behavior and shape the communities we live in. Despite their importance, data about signed relations is rare and commonly gathered through surveys. Interaction data is more abundant, for instance, in the form of proximity or communication data. So far, though, it could not be utilized to detect signed relations. In this paper, we show how the underlying signed relations can be extracted with such data. Employing a statistical network approach, we construct networks of signed relations in five communities. We then show that these relations correspond to the ones reported by the individuals themselves. Additionally, using inferred relations, we study the homophily of individuals with respect to gender, religious beliefs, and financial backgrounds. Finally, we study group cohesion in the analyzed communities by evaluating triad statistics in the reconstructed signed network.

Rational inferences about social valuation

The decisions made by other people can contain information about the value they assign to our welfare-for example how much they are willing to sacrifice to make us better off. An emerging body of research suggests that we extract and use this information, responding more favorably to those who sacrifice more even if they provide us with less. The magnitude of their trade-offs governs our social responses to them-including partner choice, giving, and anger. This implies that people have well-designed cognitive mechanisms for estimating the weight someone else assigns to their welfare, even when the amounts at stake vary and the information is noisy or sparse. We tested this hypothesis in two studies (N=200; US samples) by asking participants to observe a partner make two trade-offs, and then predict the partner's decisions in other trials. Their predictions were compared to those of a model that uses statistically optimal procedures, operationalized as a Bayesian ideal observer. As predicted, (i) the estimates people made from sparse evidence matched those of the ideal observer, and (ii) lower welfare trade-offs elicited more anger from participants, even when their total payoffs were held constant. These results support the view that people efficiently update their representations of how much others value them. They also provide the most direct test to date of a key assumption of the recalibrational theory of anger: that anger is triggered by cues of low valuation, not by the infliction of costs.

Evolution of norms for judging social behavior

Reputations provide a powerful mechanism to sustain cooperation, as individuals cooperate with those of good social standing. But how should someone's reputation be updated as we observe their social behavior, and when will a population converge on a shared norm for judging behavior? Here, we develop a mathematical model of cooperation conditioned on reputations, for a population that is stratified into groups. Each group may subscribe to a different social norm for assessing reputations and so norms compete as individuals choose to move from one group to another. We show that a group initially comprising a minority of the population may nonetheless overtake the entire population-especially if it adopts the Stern Judging norm, which assigns a bad reputation to individuals who cooperate with those of bad standing. When individuals do not change group membership, stratifying reputation information into groups tends to destabilize cooperation, unless individuals are strongly insular and favor in-group social interactions. We discuss the implications of our results for the structure of information flow in a population and for the evolution of social norms of judgment.

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.

Grouping promotes both partnership and rivalry with long memory in direct reciprocity

Biological and social scientists have long been interested in understanding how to reconcile individual and collective interests in the iterated Prisoner's Dilemma. Many effective strategies have been proposed, and they are often categorized into one of two classes, 'partners' and 'rivals.' More recently, another class, 'friendly rivals,' has been identified in longer-memory strategy spaces. Friendly rivals qualify as both partners and rivals: They fully cooperate with themselves, like partners, but never allow their co-players to earn higher payoffs, like rivals. Although they have appealing theoretical properties, it is unclear whether they would emerge in an evolving population because most previous works focus on the memory-one strategy space, where no friendly rival strategy exists. To investigate this issue, we have conducted evolutionary simulations in well-mixed and group-structured populations and compared the evolutionary dynamics between memory-one and longer-memory strategy spaces. In a well-mixed population, the memory length does not make a major difference, and the key factors are the population size and the benefit of cooperation. Friendly rivals play a minor role because being a partner or a rival is often good enough in a given environment. It is in a group-structured population that memory length makes a stark difference: When longer-memory strategies are available, friendly rivals become dominant, and the cooperation level nearly reaches a maximum, even when the benefit of cooperation is so low that cooperation would not be achieved in a well-mixed population. This result highlights the important interaction between group structure and memory lengths that drive the evolution of cooperation.

Mutation enhances cooperation in direct reciprocity

Direct reciprocity is a powerful mechanism for the evolution of cooperation based on repeated interactions between the same individuals. But high levels of cooperation evolve only if the benefit-to-cost ratio exceeds a certain threshold that depends on memory length. For the best-explored case of one-round memory, that threshold is two. Here, we report that intermediate mutation rates lead to high levels of cooperation, even if the benefit-to-cost ratio is only marginally above one, and even if individuals only use a minimum of past information. This surprising observation is caused by two effects. First, mutation generates diversity which undermines the evolutionary stability of defectors. Second, mutation leads to diverse communities of cooperators that are more resilient than homogeneous ones. This finding is relevant because many real-world opportunities for cooperation have small benefit-to-cost ratios, which are between one and two, and we describe how direct reciprocity can attain cooperation in such settings. Our result can be interpreted as showing that diversity, rather than uniformity, promotes evolution of cooperation.

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'.

Quantitative assessment can stabilize indirect reciprocity under imperfect information

The field of indirect reciprocity investigates how social norms can foster cooperation when individuals continuously monitor and assess each other's social interactions. By adhering to certain social norms, cooperating individuals can improve their reputation and, in turn, receive benefits from others. Eight social norms, known as the "leading eight," have been shown to effectively promote the evolution of cooperation as long as information is public and reliable. These norms categorize group members as either 'good' or 'bad'. In this study, we examine a scenario where individuals instead assign nuanced reputation scores to each other, and only cooperate with those whose reputation exceeds a certain threshold. We find both analytically and through simulations that such quantitative assessments are error-correcting, thus facilitating cooperation in situations where information is private and unreliable. Moreover, our results identify four specific norms that are robust to such conditions, and may be relevant for helping to sustain cooperation in natural populations.

Group reciprocity and the evolution of stereotyping

Stereotypes are generalized beliefs about groups of people, which are used to make decisions and judgements about them. Although such heuristics can be useful when decisions must be made quickly, or when information is lacking, they can also serve as the basis for prejudice and discrimination. In this paper, we study the evolution of stereotypes through group reciprocity. We characterize the warmth of a stereotype as the willingness to cooperate with an individual based solely on the identity of the group they belong to. We show that when stereotype groups are large, such group reciprocity is less likely to evolve, and stereotypes tend to be negative. We also show that, even when stereotypes are broadly positive, individuals are often overly pessimistic about the willingness of those they stereotype to cooperate. We then show that the tendency for stereotyping itself to evolve is driven by the costs of cognition, so that more people are stereotyped with greater coarseness as costs increase. Finally we show that extrinsic 'shocks', in which the benefits of cooperation are suddenly reduced, can cause stereotype warmth and judgement bias to turn sharply negative, consistent with the view that economic and other crises are drivers of out-group animosity.

The impact of social comparison and (un)fairness on upstream indirect reciprocity: Evidence from ERP

Event-related potential (ERP) technology and the dictator game paradigm are used to explore the formation mechanism of upstream indirect reciprocity behaviors. We design a within subject experiment of 3 (social comparison: upward versus parallel versus downward) × 2 (treatment: fair versus unfair) involving 49 subjects. In the first round of allocations, subjects are forced to accept a monetary amount allocated to them by another player. In the second round, subjects assume the role of allocator and divide a monetary amount between themselves and a third party. Our results show the following: 1) Having received fair treatment from someone else, individuals engaged in downward comparison are more inclined to reciprocate the fairness they had received to a third party compared to individuals in parallel and upward comparison conditions. If individuals receive unfair treatment, they tend to repeat this behavior to a third party regardless of which social comparison condition they are in; 2) Under the condition of upward comparison, individuals receiving unfair treatment exhibit greater FRN amplitude and less P300 amplitude, but in parallel and downward comparison conditions, there is no significance in FRN and P300 amplitude between individuals receiving fair and unfair treatment.

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.

Evolution of cooperation through cumulative reciprocity

Reciprocity is a simple principle for cooperation that explains many of the patterns of how humans seek and receive help from each other. To capture reciprocity, traditional models often assume that individuals use simple strategies with restricted memory. These memory-1 strategies are mathematically convenient, but they miss important aspects of human reciprocity, where defections can have lasting effects. Here we instead propose a strategy of cumulative reciprocity. Cumulative reciprocators count the imbalance of cooperation across their previous interactions with their opponent. They cooperate as long as this imbalance is sufficiently small. Using analytical and computational methods, we show that this strategy can sustain cooperation in the presence of errors, that it enforces fair outcomes and that it evolves in hostile environments. Using an economic experiment, we confirm that cumulative reciprocity is more predictive of human behaviour than several classical strategies. The basic principle of cumulative reciprocity is versatile and can be extended to a range of social dilemmas.

Interaction between games give rise to the evolution of moral norms of cooperation

In many biological populations, such as human groups, individuals face a complex strategic setting, where they need to make strategic decisions over a diverse set of issues and their behavior in one strategic context can affect their decisions in another. This raises the question of how the interaction between different strategic contexts affects individuals’ strategic choices and social norms? To address this question, I introduce a framework where individuals play two games with different structures and decide upon their strategy in a second game based on their knowledge of their opponent’s strategy in the first game. I consider both multistage games, where the same opponents play the two games consecutively, and reputation-based model, where individuals play their two games with different opponents but receive information about their opponent’s strategy. By considering a case where the first game is a social dilemma, I show that when the second game is a coordination or anti-coordination game, the Nash equilibrium of the coupled game can be decomposed into two classes, a defective equilibrium which is composed of two simple equilibrium of the two games, and a cooperative equilibrium, in which coupling between the two games emerge and sustain cooperation in the social dilemma. For the existence of the cooperative equilibrium, the cost of cooperation should be smaller than a value determined by the structure of the second game. Investigation of the evolutionary dynamics shows that a cooperative fixed point exists when the second game belongs to coordination or anti-coordination class in a mixed population. However, the basin of attraction of the cooperative fixed point is much smaller for the coordination class, and this fixed point disappears in a structured population. When the second game belongs to the anti-coordination class, the system possesses a spontaneous symmetry-breaking phase transition above which the symmetry between cooperation and defection breaks. A set of cooperation supporting moral norms emerges according to which cooperation stands out as a valuable trait. Notably, the moral system also brings a more efficient allocation of resources in the second game. This observation suggests a moral system has two different roles: Promotion of cooperation, which is against individuals’ self-interest but beneficial for the population, and promotion of organization and order, which is at both the population’s and the individual’s self-interest. Interestingly, the latter acts like a Trojan horse: Once established out of individuals’ self-interest, it brings the former with itself. Importantly, the fact that the evolution of moral norms depends only on the cost of cooperation and is independent of the benefit of cooperation implies that moral norms can be harmful and incur a pure collective cost, yet they are just as effective in promoting order and organization. Finally, the model predicts that recognition noise can have a surprisingly positive effect on the evolution of moral norms and facilitates cooperation in the Snow Drift game in structured populations.

How do moral norms spontaneously evolve in the presence of selfish incentives? An answer to this question is provided by the observation that moral systems have two distinct functions: Besides encouraging self-sacrificing cooperation, they also bring organization and order into the societies. In contrast to the former, which is costly for the individuals but beneficial for the group, the latter is beneficial for both the group and the individuals. A simple evolutionary model suggests this latter aspect is what makes a moral system evolve based on the individuals’ self-interest. However, a moral system behaves like a Trojan horse: Once established out of the individuals’ self-interest to promote order and organization, it also brings self-sacrificing cooperation.

The marmoset as a model for investigating the neural basis of social cognition in health and disease

Social-cognitive processes facilitate the use of environmental cues to understand others, and to be understood by others. Animal models provide vital insights into the neural underpinning of social behaviours. To understand social cognition at even deeper behavioural, cognitive, neural, and molecular levels, we need to develop more representative study models, which allow testing of novel hypotheses using human-relevant cognitive tasks. Due to their cooperative breeding system and relatively small size, common marmosets (Callithrix jacchus) offer a promising translational model for such endeavours. In addition to having social behavioural patterns and group dynamics analogous to those of humans, marmosets have cortical brain areas relevant for the mechanistic analysis of human social cognition, albeit in simplified form. Thus, they are likely suitable animal models for deciphering the physiological processes, connectivity and molecular mechanisms supporting advanced cognitive functions. Here, we review findings emerging from marmoset social and behavioural studies, which have already provided significant insights into executive, motivational, social, and emotional dysfunction associated with neurological and psychiatric disorders.

Cooperation in alternating interactions with memory constraints

In repeated social interactions, individuals often employ reciprocal strategies to maintain cooperation. To explore the emergence of reciprocity, many theoretical models assume synchronized decision making. In each round, individuals decide simultaneously whether to cooperate or not. Yet many manifestations of reciprocity in nature are asynchronous. Individuals provide help at one time and receive help at another. Here, we explore such alternating games in which players take turns. We mathematically characterize all Nash equilibria among memory-one strategies. Moreover, we use evolutionary simulations to explore various model extensions, exploring the effect of discounted games, irregular alternation patterns, and higher memory. In all cases, we observe that mutual cooperation still evolves for a wide range of parameter values. However, compared to simultaneous games, alternating games require different strategies to maintain cooperation in noisy environments. Moreover, none of the respective strategies are evolutionarily stable.

In many instances of reciprocity, individuals cooperate in turns. Here, the authors analyze the equilibria and the dynamics of such alternating games, and in particular describe all strategies with one-round memory that maintain cooperation.

Adaptive Empathy: A Model for Learning Empathic Responses in Response to Feedback

Empathy is usually deployed in social interactions. Nevertheless, common measures and examinations of empathy study this construct in isolation from the person in distress. In this article we seek to extend the field of examination to include both empathizer and target to determine whether and how empathic responses are affected by feedback and learned through interaction. Building on computational approaches in feedback-based adaptations (e.g., no feedback, model-free and model-based learning), we propose a framework for understanding how empathic responses are learned on the basis of feedback. In this framework, adaptive empathy, defined as the ability to adapt one's empathic responses, is a central aspect of empathic skills and can provide a new dimension to the evaluation and investigation of empathy. By extending existing neural models of empathy, we suggest that adaptive empathy may be mediated by interactions between the neural circuits associated with valuation, shared distress, observation-execution, and mentalizing. Finally, we propose that adaptive empathy should be considered a prominent facet of empathic capabilities with the potential to explain empathic behavior in health and psychopathology.

Social norms in indirect reciprocity with ternary reputations

Indirect reciprocity is a key mechanism that promotes cooperation in social dilemmas by means of reputation. Although it has been a common practice to represent reputations by binary values, either ‘good’ or ‘bad’, such a dichotomy is a crude approximation considering the complexity of reality. In this work, we studied norms with three different reputations, i.e., ‘good’, ‘neutral’, and ‘bad’. Through massive supercomputing for handling more than thirty billion possibilities, we fully identified which norms achieve cooperation and possess evolutionary stability against behavioural mutants. By systematically categorizing all these norms according to their behaviours, we found similarities and dissimilarities to their binary-reputation counterpart, the leading eight. We obtained four rules that should be satisfied by the successful norms, and the behaviour of the leading eight can be understood as a special case of these rules. A couple of norms that show counter-intuitive behaviours are also presented. We believe the findings are also useful for designing successful norms with more general reputation systems.

Evolution of cooperation and consistent personalities in public goods games

The evolution of cooperation has remained an important problem in evolutionary theory and social sciences. In this regard, a curious question is why consistent cooperative and defective personalities exist and if they serve a role in the evolution of cooperation? To shed light on these questions, here, I consider a population of individuals who possibly play two consecutive rounds of public goods game, with different enhancement factors. Importantly, individuals have independent strategies in the two rounds. However, their strategy in the first round affects the game they play in the second round. I consider two different scenarios where either only first-round cooperators play a second public goods game, or both first-round cooperators and first-round defectors play a second public goods game, but in different groups. The first scenario can be considered a reward dilemma, and the second can be considered an assortative public goods game but with independent strategies of the individuals in the two rounds. Both models show cooperators can survive either in a fixed point or through different periodic orbits. Interestingly, due to the emergence of a correlation between the strategies of the individuals in the two rounds, individuals develop consistent personalities during the evolution. This, in turn, helps cooperation to flourish. These findings shed new light on the evolution of cooperation and show how consistent cooperative and defective personalities can evolve and play a positive role in solving social dilemmas.

The evolution of indirect reciprocity under action and assessment generosity

Indirect reciprocity is a mechanism for the evolution of cooperation based on social norms. This mechanism requires that individuals in a population observe and judge each other's behaviors. Individuals with a good reputation are more likely to receive help from others. Previous work suggests that indirect reciprocity is only effective when all relevant information is reliable and publicly available. Otherwise, individuals may disagree on how to assess others, even if they all apply the same social norm. Such disagreements can lead to a breakdown of cooperation. Here we explore whether the predominantly studied 'leading eight' social norms of indirect reciprocity can be made more robust by equipping them with an element of generosity. To this end, we distinguish between two kinds of generosity. According to assessment generosity, individuals occasionally assign a good reputation to group members who would usually be regarded as bad. According to action generosity, individuals occasionally cooperate with group members with whom they would usually defect. Using individual-based simulations, we show that the two kinds of generosity have a very different effect on the resulting reputation dynamics. Assessment generosity tends to add to the overall noise and allows defectors to invade. In contrast, a limited amount of action generosity can be beneficial in a few cases. However, even when action generosity is beneficial, the respective simulations do not result in full cooperation. Our results suggest that while generosity can favor cooperation when individuals use the most simple strategies of reciprocity, it is disadvantageous when individuals use more complex social norms.

Direct and indirect reciprocity among individuals and groups

Direct and indirect reciprocity are two fundamental mechanisms that promote prosocial behavior within groups and across societies. Here, we review recent work that illustrates how a (direct and indirect) reciprocity framework can illuminate our understanding of several factors related to prosocial behavior - namely group membership, gossip, and third-party punishment. We propose that each of these factors can promote prosocial behavior via proximate psychological mechanisms related to direct and indirect reciprocity: reputational concern, expectations, and anticipation of future interaction. Finally, we discuss the implications of adopting such a framework and highlight a number of avenues for future research.

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.