A Review of Theoretical Studies on Indirect Reciprocity

Many-strategy games in groups with relatives and the evolution of coordinated cooperation

Humans often cooperate in groups with friends and family members with varying degrees of genetic relatedness. Past kin selection can also be relevant to interactions between strangers, explaining how the cooperation first arose in the ancestral population. However, modelling the effects of relatedness is difficult when the benefits of cooperation scale nonlinearly with the number of cooperators (e.g., economies of scale). Here, we present a direct fitness method for rigorously accounting for kin selection in n-player interactions with m discrete strategies, where a genetically homophilic group-formation model is used to calculate the necessary higher-order relatedness coefficients. Our approach allows us to properly account for non-additive fitness effects between relatives (synergy). Analytical expressions for dynamics are obtained, and they can be solved numerically for modestly sized groups and numbers of strategies. We illustrate with an example where group members can verbally agree (cheap talk) to contribute to a public good with a sigmoidal benefit function, and we find that such coordinated cooperation is favoured by kin selection. As interactions switched from family to strangers, in order for coordinated cooperation to persist and for the population to resist invasion by liars, either some level of homophily must be maintained or following through on the agreement must be in the self-interests of contributors. Our approach is useful for scenarios where fitness effects are non-additive and the strategies are best modelled in a discrete way, such as behaviours that require a cognitive 'leap' of insight into the situation (e.g., shared intentionality, punishment).

Evolution of indirect reciprocity under emotion expression

Do emotion expressions impact the evolution of cooperation? Indirect Reciprocity offers a solution to the cooperation dilemma with prior work focusing on the role of social norms in propagating others' reputations and contributing to evolutionarily stable cooperation. Recent experimental studies, however, show that emotion expressions shape pro-social behaviour, communicate one's intentions to others, and serve an error-correcting function; yet, the role of emotion signals in the evolution of cooperation remains unexplored. We present the first model of IR based on evolutionary game theory that exposes how emotion expressions positively influence the evolution of cooperation, particularly in scenarios of frequent errors. Our findings provide evolutionary support for the existence of emotion-based social norms, which help foster cooperation among unrelated individuals.

Costly punishment sustains indirect reciprocity under low defection detectability

Cooperation is fundamental to human societies, and indirect reciprocity, where individuals cooperate to build a positive reputation for future benefits, plays a key role in promoting it. Previous theoretical and experimental studies have explored both the effectiveness and limitations of costly punishment in sustaining cooperation. While empirical observations show that costly punishment by third parties is common, some theoretical models suggest it may not be effective in the context of indirect reciprocity, raising doubts about its potential to enhance cooperation. In this study, we theoretically investigate the conditions under which costly punishment is effective. Building on a previous model, we introduce a new type of error in perceiving actions, where defection may be mistakenly perceived as cooperation. This extension models a realistic scenario where defectors have a strong incentive to disguise their defection as cooperation. Our analysis reveals that when defection is difficult to detect, norms involving costly punishment can emerge as the most efficient evolutionarily stable strategies. These findings demonstrate that costly punishment can play a crucial role in promoting cooperation within indirect reciprocity.

Convergence of reputations under indirect reciprocity

Previous research has shown how indirect reciprocity can promote cooperation through evolutionary game theoretic models. Most work in this field assumes a separation of time-scales: individuals' reputations equilibrate at a fast time scale for given frequencies of strategies while the strategies change slowly according to the replicator dynamics. Much of the previous research has focused on the behaviour and stability of equilibria for the replicator dynamics. Here we focus on the underlying reputational dynamics that occur on a fast time scale. We describe reputational dynamics as systems of differential equations and conduct stability analyses on their equilibria. We prove that reputations converge to a unique equilibrium under a solitary observer model for each of the five standard norms and whether assessments are public or private. These results confirm a crucial but previously understudied assumption underlying the theory of indirect reciprocity for the most studied set of norms.

Evolutionary mechanisms that promote cooperation may not promote social welfare

Understanding the emergence of prosocial behaviours among self-interested individuals is an important problem in many scientific disciplines. Various mechanisms have been proposed to explain the evolution of such behaviours, primarily seeking the conditions under which a given mechanism can induce highest levels of cooperation. As these mechanisms usually involve costs that alter individual pay-offs, it is, however, possible that aiming for highest levels of cooperation might be detrimental for social welfare-the latter broadly defined as the total population pay-off, taking into account all costs involved for inducing increased prosocial behaviours. Herein, by comparing stochastic evolutionary models of two well-established mechanisms of prosocial behaviour-namely, peer and institutional incentives-we demonstrate that the objectives of maximizing cooperation and of maximizing social welfare are often misaligned. First, while peer punishment is often more effective than peer reward in promoting cooperation-especially with a higher impact-to-cost ratio-the opposite is true for social welfare. In fact, welfare typically decreases (increases) with this ratio for punishment (reward). Second, for institutional incentives, while maintaining similar levels of cooperation, rewards result in positive social welfare across a much broader range of parameters. Furthermore, both types of incentives often achieve optimal social welfare when their impact is moderate rather than maximal, indicating that careful planning is essential for costly institutional mechanisms to optimize social outcomes. These findings are consistent across varying mutation rates, selection intensities and game configurations. Overall, we argue for the need of adopting social welfare as the main optimization objective when designing and implementing evolutionary mechanisms for social and collective goods.

The evolution of private reputations in information-abundant landscapes

Reputations are critical to human societies, as individuals are treated differently based on their social standing1,2. For instance, those who garner a good reputation by helping others are more likely to be rewarded by third parties3-5. Achieving widespread cooperation in this way requires that reputations accurately reflect behaviour6 and that individuals agree about each other's standings7. With few exceptions8-10, theoretical work has assumed that information is limited, which hinders consensus7,11 unless there are mechanisms to enforce agreement, such as empathy12, gossip13-15 or public institutions16. Such mechanisms face challenges in a world where empathy, effective communication and institutional trust are compromised17-19. However, information about others is now abundant and readily available, particularly through social media. Here we demonstrate that assigning private reputations by aggregating several observations of an individual can accurately capture behaviour, foster emergent agreement without enforcement mechanisms and maintain cooperation, provided individuals exhibit some tolerance for bad actions. This finding holds for both first- and second-order norms of judgement and is robust even when norms vary within a population. When the aggregation rule itself can evolve, selection indeed favours the use of several observations and tolerant judgements. Nonetheless, even when information is freely accessible, individuals do not typically evolve to use all of it. This method of assessing reputations-'look twice, forgive once', in a nutshell-is simple enough to have arisen early in human culture and powerful enough to persist as a fundamental component of social heuristics.

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.

Norms prioritizing positive assessments are likely to maintain cooperation in private indirect reciprocity

Exploring the evolutionary mechanisms of cooperation in societies where reputational consensus cannot be assumed, as in divided societies, is important for understanding the basic principles of human behavior in modern societies. Indirect reciprocity provides a major explanatory mechanism, but most studies have focused on how donors, i.e., one who decides whether to donate (cooperate or help) to a recipient or do nothing, are assessed. It is natural to think that there is no consensus among assessors in our society, and there is no reason to update only donor assessments when updating assessments. We constructed an agent-based model that enables updating of both donors' and recipients' images. Our exhaustive simulations showed that the well analyzed assessment rules updating donors' images are only second best to an assessment rule updating bad images in most likely for maintaining cooperative regimes. Such a social norm that prioritizes a positive assessment is considered tolerant, which is also consistent with previous studies arguing that tolerant evaluation is important in private-assessment schemes.

Indirect reciprocity with Bayesian reasoning and biases

Reputations can foster cooperation by indirect reciprocity: if I am good to you then others will be good to me. But this mechanism for cooperation in one-shot interactions only works when people agree on who is good and who is bad. Errors in actions or assessments can produce disagreements about reputations, which can unravel the positive feedback loop between social standing and pro-social behaviour. Cooperators can end up punished and defectors rewarded. Public reputation systems and empathy are two possible mechanisms to promote agreement about reputations. Here we suggest an alternative: Bayesian reasoning by observers. By taking into account the probabilities of errors in action and observation and their prior beliefs about the prevalence of good people in the population, observers can use Bayesian reasoning to determine whether or not someone is good. To study this scenario, we develop an evolutionary game theoretical model in which players use Bayesian reasoning to assess reputations, either publicly or privately. We explore this model analytically and numerically for five social norms (Scoring, Shunning, Simple Standing, Staying, and Stern Judging). We systematically compare results to the case when agents do not use reasoning in determining reputations. We find that Bayesian reasoning reduces cooperation relative to non-reasoning, except in the case of the Scoring norm. Under Scoring, Bayesian reasoning can promote coexistence of three strategic types. Additionally, we study the effects of optimistic or pessimistic biases in individual beliefs about the degree of cooperation in the population. We find that optimism generally undermines cooperation whereas pessimism can, in some cases, promote cooperation.

Indirect reciprocity with abductive reasoning

Indirect reciprocity is a reputational mechanism through which cooperative behavior can be promoted amongst a group of individuals. However, in order for this mechanism to effectively do so, cheating must be appropriately punished and cooperating appropriately rewarded. Errors in assessments and actions can hinder this process. In such a setting, individuals might try to reason about evidence to assign reputations given the possibility of errors. Here, we consider a well-established theory of reasoning used to combine evidence, abductive reasoning, as a possible means by which such errors can be circumvented. Specifically, we use Dempster-Shafer theory to model individuals who account for possible errors by combining information about their beliefs about the status of the population and the errors rates and then choose the simplest scenario that could explain their observations in the context of these beliefs. We investigate the effectiveness of abductive reasoning at promoting cooperation for five social norms: Scoring, Shunning, Simple Standing, Staying, and Stern Judging. We find that, generally, abductive reasoning can outperform non-reasoning models at ameliorating the effects of the aforementioned challenges and promote higher levels of cooperation under low-error conditions. However, for high-error conditions, we find that abductive reasoning can undermine cooperation. Furthermore, we also find that a degree of bias towards believing previously held reputations can help sustain cooperation.

Group Formation and the Evolution of Human Social Organization

Humans operate in groups that are oftentimes nested in multilayered collectives such as work units within departments and companies, neighborhoods within cities, and regions within nation states. With psychological science mostly focusing on proximate reasons for individuals to join existing groups and how existing groups function, we still poorly understand why groups form ex nihilo, how groups evolve into complex multilayered social structures, and what explains fission-fusion dynamics. Here we address group formation and the evolution of social organization at both the proximate and ultimate level of analysis. Building on models of fitness interdependence and cooperation, we propose that socioecologies can create positive interdependencies among strangers and pave the way for the formation of stable coalitions and groups through reciprocity and reputation-based partner selection. Such groups are marked by in-group bounded, parochial cooperation together with an array of social institutions for managing the commons, allowing groups to scale in size and complexity while avoiding the breakdown of cooperation. Our analysis reveals how distinct group cultures can endogenously emerge from reciprocal cooperation, shows that social identification and group commitment are likely consequences rather than causes of group cooperation, and explains when intergroup relations gravitate toward peaceful coexistence, integration, or conflict.

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.

Co-evolution of conditional cooperation and social norm

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

Individuals reciprocate negative actions revealing negative upstream reciprocity

Indirect reciprocity is widely recognized as a mechanism for explaining cooperation and can be divided into two sub-concepts: downstream and upstream reciprocity. Downstream reciprocity is supported by reputation; if someone sees you helping someone else, the person who sees this will think higher of you, and you will be more likely to be helped. Upstream reciprocity is helping someone because you are being helped by somebody else, which often happens in everyday life and experimental games. This paper focuses on the behavior of "take" and examines negative upstream reciprocity using an upstream reciprocity framework. The term "take" is defined as "to steal rather than give resources to others." "If something is taken from you, do you take from others?" is an important extension for indirect reciprocity research; subsequently, this paper discusses experiments conducted on whether negative upstream reciprocity is chained and what causes it. The results demonstrated differences between positive and negative upstream reciprocity. In analyzing the data of nearly 600 participants to determine the extent to which negative upstream reciprocity is observed and the causes of negative upstream reciprocity, the study found that If individual A takes resources from individual B, then B is more likely to take resources from a third-party, individual C. Notably, some causes of positive upstream reciprocity were found to have no effect or the opposite effect on negative upstream reciprocity. The results also demonstrate that the first person to take can cause a chain reaction. This paper demonstrates the importance of the first person not taking from someone else and suggests the need to consider various behavioral options for future research on cooperation.

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

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

Score-mediated mutual consent and indirect reciprocity

Helping strangers at a cost to oneself is a hallmark of many human interactions, but difficult to justify from the viewpoint of natural selection, particularly in anonymous one-shot interactions. Reputational scoring can provide the necessary motivation via "indirect reciprocity," but maintaining reliable scores requires close oversight to prevent cheating. We show that in the absence of such supervision, it is possible that scores might be managed by mutual consent between the agents themselves instead of by third parties. The space of possible strategies for such "consented" score changes is very large but, using a simple cooperation game, we search it, asking what kinds of agreement can i) invade a population from rare and ii) resist invasion once common. We prove mathematically and demonstrate computationally that score mediation by mutual consent does enable cooperation without oversight. Moreover, the most invasive and stable strategies belong to one family and ground the concept of value by incrementing one score at the cost of the other, thus closely resembling the token exchange that underlies money in everyday human transactions. The most successful strategy has the flavor of money except that agents without money can generate new score if they meet. This strategy is evolutionarily stable, and has higher fitness, but is not physically realizable in a decentralized way; when conservation of score is enforced more money-like strategies dominate. The equilibrium distribution of scores under any of this family of strategies is geometric, meaning that agents with score 0 are inherent to money-like strategies.

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

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

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.

The evolution of universal cooperation

Humans work together in groups to tackle shared problems and contribute to local club goods that benefit other group members. Whereas benefits from club goods remain group bound, groups are often nested in overarching collectives that face shared problems like pandemics or climate change. Such challenges require individuals to cooperate across group boundaries, raising the question how cooperation can transcend beyond confined groups. Here, we show how frequent intergroup interactions allow groups to transition from group-bound to universal cooperation. With frequent intergroup interactions, reciprocity of cooperative acts permeates group boundaries and enables the evolution of universal cooperation. As soon as intergroup interactions take place frequently, people start to selectively reward cooperation aimed at benefitting everyone, irrespective of their group membership. Simulations further show that it becomes more difficult to overcome group-bound cooperation when populations are fragmented into many small groups. Our findings reveal important prerequisites for the evolution of universal cooperation.

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.

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.

Strategic complexity and cognitive skills affect brain response in interactive decision-making

Deciding the best action in social settings requires decision-makers to consider their and others’ preferences, since the outcome depends on the actions of both. Numerous empirical investigations have demonstrated variability of behavior across individuals in strategic situations. While prosocial, moral, and emotional factors have been intensively investigated to explain this diversity, neuro-cognitive determinants of strategic decision-making and their relation with intelligence remain mostly unknown. This study presents a new model of the process of strategic decision-making in repeated interactions, first providing a precise measure of the environment’s complexity, and then analyzing how this complexity affects subjects’ performance and neural response. The results confirm the theoretical predictions of the model. The frequency of deviations from optimal behavior is explained by a combination of higher complexity of the strategic environment and cognitive skills of the individuals. Brain response correlates with strategic complexity, but only in the subgroups with higher cognitive skills. Furthermore, neural effects were only observed in a fronto-parietal network typically involved in single-agent tasks (the Multiple Demand Network), thus suggesting that neural processes dealing with cognitively demanding individual tasks also have a central role in interactive decision-making. Our findings contribute to understanding how cognitive factors shape strategic decision-making and may provide the neural pathway of the reported association between strategic sophistication and fluid intelligence.

Costly incentives design from an institutional perspective: cooperation, sustainability and affluence

Incentives are usually introduced by the regulator entity (third-party), to promote cooperation in a market. The implementation of incentives is always costly and thus might fail to be enforced sustainably. This work aims at exploring the effects of incentives from an institutional perspective, while coping with the scenario where the third-party is part of the system but not composed by players. The evolutionary game theory (EGT) framework is applied to identify the incentives that lead to pure cooperation. In contrast to traditional EGT, this paper introduces an elimination mechanism that can reduce the market size. The incentives identified in the EGT analysis are further examined in simulation experiments which measure the market size, affluence and sustainability. The findings show: (1) light punishment leads to a reduction of the market size, yet heavier punishment is beneficial to the market size and wealth; (2) mixed incentives will generally lead to different wealth of the third party and of the participants. While under moderate strength, the wealth of both parties is the same and their overall wealth is maximal; (3) for sustainability, pure punishment (resp. reward) is sustainable (resp. unsustainable), the sustainability of mixed incentives depends on both their strength and agents’ rationality level.

Explaining costly religious practices: credibility enhancing displays and signaling theories

This paper examines and contrasts two closely related evolutionary explanations in human behaviour: signalling theory, and the theory of Credibility Enhancing Displays (CREDs). Both have been proposed to explain costly, dangerous, or otherwise 'extravagant' social behaviours, especially in the context of religious belief and practice, and each have spawned significant lines of empirical research. However, the relationship between these two theoretical frameworks is unclear, and research which engages both of them (especially in systematic comparison) is largely absent. In this paper we seek to address this gap at the theoretical level, examining the core differences between the two approaches and prospects and conditions for future empirical testing. We clarify the dynamical and mechanistic bases of signalling and CREDs as explanatory models and contrast the previous uses to which they have been put in the human sciences. Because of idiosyncrasies regarding those uses (especially with signalling), several commonly supposed differences and comparative advantages are actually misleading and not in fact generalisable. We also show that signalling and CREDs theories as explanatory models are not interchangeable (or reducible to one another), because of deep structural differences. As we illustrate, the proposed causal networks of each theory are distinct, with important differences in the endogeneity of various phenomena within each model and their explanatory targets. As a result, they can be seen as complementary rather than in competition. We conclude by surveying the current state of the literature and identifying the differential predictions which could underpin more comprehensive empirical comparison in future research.

Institutional incentives for the evolution of committed cooperation: ensuring participation is as important as enhancing compliance

Both conventional wisdom and empirical evidence suggest that arranging a prior commitment or agreement before an interaction takes place enhances the chance of reaching mutual cooperation. Yet it is not clear what mechanisms might underlie the participation in and compliance with such a commitment, especially when participation is costly and non-compliance can be profitable. Here, we develop a theory of participation and compliance with respect to an explicit commitment formation process and to institutional incentives where individuals, at first, decide whether or not to join a cooperative agreement to play a one-shot social dilemma game. Using a mathematical model, we determine whether and when participating in a costly commitment, and complying with it, is an evolutionarily stable strategy, resulting in high levels of cooperation. We show that, given a sufficient budget for providing incentives, rewarding of commitment compliant behaviours better promotes cooperation than punishment of non-compliant ones. Moreover, by sparing part of this budget for rewarding those willing to participate in a commitment, the overall level of cooperation can be significantly enhanced for both reward and punishment. Finally, the presence of mistakes in deciding to participate favours evolutionary stability of commitment compliance and cooperation.

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.

The benefits of being seen to help others: indirect reciprocity and reputation-based partner choice

When one individual helps another, it benefits the recipient and may also gain a reputation for being cooperative. This may induce others to favour the helper in subsequent interactions, so investing in being seen to help others may be adaptive. The best-known mechanism for this is indirect reciprocity (IR), in which the profit comes from an observer who pays a cost to benefit the original helper. IR has attracted considerable theoretical and empirical interest, but it is not the only way in which cooperative reputations can bring benefits. Signalling theory proposes that paying a cost to benefit others is a strategic investment which benefits the signaller through changing receiver behaviour, in particular by being more likely to choose the signaller as a partner. This reputation-based partner choice can result in competitive helping whereby those who help are favoured as partners. These theories have been confused in the literature. We therefore set out the assumptions, the mechanisms and the predictions of each theory for how developing a cooperative reputation can be adaptive. The benefits of being seen to be cooperative may have been a major driver of sociality, especially in humans. This article is part of the theme issue 'The language of cooperation: reputation and honest signalling'.

The complexity of human cooperation under indirect reciprocity

Indirect reciprocity (IR) is a key mechanism to understand cooperation among unrelated individuals. It involves reputations and complex information processing, arising from social interactions. By helping someone, individuals may improve their reputation, which may be shared in a population and change the predisposition of others to reciprocate in the future. The reputation of individuals depends, in turn, on social norms that define a good or bad action, offering a computational and mathematical appealing way of studying the evolution of moral systems. Over the years, theoretical and empirical research has unveiled many features of cooperation under IR, exploring norms with varying degrees of complexity and information requirements. Recent results suggest that costly reputation spread, interaction observability and empathy are determinants of cooperation under IR. Importantly, such characteristics probably impact the level of complexity and information requirements for IR to sustain cooperation. In this review, we present and discuss those recent results. We provide a synthesis of theoretical models and discuss previous conclusions through the lens of evolutionary game theory and cognitive complexity. We highlight open questions and suggest future research in this domain. This article is part of the theme issue 'The language of cooperation: reputation and honest signalling'.

The language of cooperation: reputation and honest signalling

Large-scale non-kin cooperation is a unique ingredient of human success. This type of cooperation is challenging to explain in a world of self-interested individuals. There is overwhelming empirical evidence from different disciplines that reputation and gossip promote cooperation in humans in different contexts. Despite decades of research, important details of reputation systems are still unclear. Our goal with this theme issue is to promote an interdisciplinary approach that allows us to explore and understand the evolution and maintenance of reputation systems with a special emphasis on gossip and honest signalling. The theme issue is organized around four main questions: What are the necessary conditions for reputation-based systems? What is the content and context of reputation systems? How can reputations promote cooperation? And, what is the role of gossip in maintaining reputation systems and thus cooperation? This article is part of the theme issue 'The language of cooperation: reputation and honest signalling'.

Cost efficiency of institutional incentives for promoting cooperation in finite populations

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

Reward, punishment, and prosocial behavior: Recent developments and implications

Reward and punishment change the payoff structures of social interactions and therefore can potentially play a role in promoting prosocial behavior. Yet, there are boundary conditions for them to be effective. We review recent work that addresses the conditions under which rewards and punishment can enhance prosocial behavior, the proximate and ultimate mechanisms for individuals' rewarding and punishing decisions, and the reputational and behavioral consequences of reward and punishment under noise. The reviewed evidence points to the importance of more field research on how reward and punishment can promote prosocial behavior in real-world settings. We also highlight the need to integrate different methodologies to better examine the effects of reward and punishment on prosocial behavior.

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.

Local reputation, local selection, and the leading eight norms

Humans are capable of solving cooperation problems following social norms. Social norms dictate appropriate behaviour and judgement on others in response to their previous actions and reputation. Recently, the so-called leading eight norms have been identified from many potential social norms that can sustain cooperation through a reputation-based indirect reciprocity mechanism. Despite indirect reciprocity being claimed to extend direct reciprocity in larger populations where direct experiences cannot be accumulated, the success of social norms have been analysed in models with global information and evolution. This study is the first to analyse the leading eight norms with local information and evolution. We find that the leading eight are robust against selfish players within most scenarios and can maintain a high level of cooperation also with local information and evolution. In fact, local evolution sustains cooperation under a wider set of conditions than global evolution, while local reputation does not hinder cooperation compared to global reputation. Four of the leading eight norms that do not reward justified defection offer better chances for cooperation with quick evolution, reputation with noise, larger networks, and when unconditional defectors enter the population.

Cooperation in spatial public good games depends on the locality effects of game, adaptation, and punishment

Despite intensive studies on the evolution of cooperation in spatial public goods games, there have been few investigations into locality effects in interaction games, adaptation, and punishment. Here we analyze locality effects using an agent-based model of a regular graph. Our simulation shows that a situation containing a local game, local punishment, and global adaptation leads to the most robustly cooperative regime. Further, we show an interesting feature in local punishment. Previous studies showed that a local game and global adaptation are likely to generate cooperation. However, they did not consider punishment. We show that if local punishment is introduced in spatial public goods games, a situation satisfying either local game or local adaptation is likely to generate cooperation. We thus propose two principles. One is if interactions in games can be restricted locally, it is likely to generate cooperation independent of the interaction situations on punishment and adaptation. The other is if the games must be played globally, a cooperative regime requires both local punishment and local adaptation.

Cooperation through Image Scoring: A Replication

“Image scoring” is a type of social evaluation, originally used in agent-based models, where the reputation of another is numerically assessed. This phenomenon has been studied in both theoretical models and real-life psychology experiments (using human participants). The latter are aimed to create conditions in the laboratory where image scoring can be elicited. One influential paper is that of Wedekind and Milinski (2000), WM. Our paper is a replication of that study, deliberately employing very similar methodology to the original. Accordingly, we had six groups of ten participants play an economic game. In each round, each player was randomly paired with another player whose identity was unknown. The participant was given a binary choice of either (1) donating money to that person, or (2) not donating money. In each round, the player was passively exposed to information about the past generosity of the other player. In our study, we successfully replicated the central result of WM. Participants in our replication gave significantly more money to partners with higher image scores (more generous reputations) than those with lower image scores (less generous reputations). This paper also provides a critical review of the methodology of WM and the study of image scoring.

How Reputation Systems Change the Psychological Antecedents of Fairness in Virtual Environments

Reputational systems promote pro-social behaviors, also in virtual environments, therefore their study contributes to the knowledge of social interactions. Literature findings emphasize the power of reputation in fostering fairness in many circumstances, even when its influence is not directly oriented towards specific individuals. The present study contributes to the investigation of the psychological antecedents of fairness, introducing (or not) reputation in the social dilemma framework. Although reputational systems usually influence fairness dynamics, there are also socio-psychological characteristics that can play a role, affecting the adhesion to the norm online. To investigate their effects, we employed a virtual bargaining game that could include a reputational system depending on the experimental condition. Results show that the participant’s fairness could be significantly influenced by socio-psychological and demographic characteristics, as well as personality traits. Reputation seems to decrease fairness in those individuals who report high levels of Neuroticism and Openness. At the same time, high values of Self-Efficacy appear to be more likely associated with unfair behaviors when reputation is off the bargaining. Finally, Age and Sense of Community emerge as fairness promoters regardless of the experimental condition.