Indirect reciprocity undermines indirect reciprocity destabilizing large-scale cooperation.

Previous models suggest that indirect reciprocity (reputation) can stabilize large-scale human cooperation [K. Panchanathan, R. Boyd, Nature 432, 499-502 (2004)]. The logic behind these models and experiments [J. Gross et al., Sci. Adv. 9, eadd8289 (2023) and O. P. Hauser, A. Hendriks, D. G. Rand, M. A. Nowak, Sci. Rep. 6, 36079 (2016)] is that a strategy in which individuals conditionally aid others based on their reputation for engaging in costly cooperative behavior serves as a punishment that incentivizes large-scale cooperation without the second-order free-rider problem. However, these models and experiments fail to account for individuals belonging to multiple groups with reputations that can be in conflict. Here, we extend these models such that individuals belong to a smaller, "local" group embedded within a larger, "global" group. This introduces competing strategies for conditionally aiding others based on their cooperative behavior in the local or global group. Our analyses reveal that the reputation for cooperation in the smaller local group can undermine cooperation in the larger global group, even when the theoretical maximum payoffs are higher in the larger global group. This model reveals that indirect reciprocity alone is insufficient for stabilizing large-scale human cooperation because cooperation at one scale can be considered defection at another. These results deepen the puzzle of large-scale human cooperation.

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.

A mechanistic model of gossip, reputations, and cooperation.

Social reputations facilitate cooperation: those who help others gain a good reputation, making them more likely to receive help themselves. But when people hold private views of one another, this cycle of indirect reciprocity breaks down, as disagreements lead to the perception of unjustified behavior that ultimately undermines cooperation. Theoretical studies often assume population-wide agreement about reputations, invoking rapid gossip as an endogenous mechanism for reaching consensus. However, the theory of indirect reciprocity lacks a mechanistic description of how gossip actually generates consensus. Here, we develop a mechanistic model of gossip-based indirect reciprocity that incorporates two alternative forms of gossip: exchanging information with randomly selected peers or consulting a single gossip source. We show that these two forms of gossip are mathematically equivalent under an appropriate transformation of parameters. We derive an analytical expression for the minimum amount of gossip required to reach sufficient consensus and stabilize cooperation. We analyze how the amount of gossip necessary for cooperation depends on the benefits and costs of cooperation, the assessment rule (social norm), and errors in reputation assessment, strategy execution, and gossip transmission. Finally, we show that biased gossip can either facilitate or hinder cooperation, depending on the direction and magnitude of the bias. Our results contribute to the growing literature on cooperation facilitated by communication, and they highlight the need to study strategic interactions coupled with the spread of social information.

Explaining the evolution of gossip.

Gossip, the exchange of personal information about absent third parties, is ubiquitous in human societies. However, the evolution of gossip remains a puzzle. The current article proposes an evolutionary cycle of gossip and uses an agent-based evolutionary game-theoretic model to assess it. We argue that the evolution of gossip is the joint consequence of its reputation dissemination and selfishness deterrence functions. Specifically, the dissemination of information about individuals' reputations leads more individuals to condition their behavior on others' reputations. This induces individuals to behave more cooperatively toward gossipers in order to improve their reputations. As a result, gossiping has an evolutionary advantage that leads to its proliferation. The evolution of gossip further facilitates these two functions of gossip and sustains the evolutionary cycle.

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.

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.

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.

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.

Indirect reciprocity with simple records.

Indirect reciprocity is a foundational mechanism of human cooperation. Existing models of indirect reciprocity fail to robustly support social cooperation: Image-scoring models fail to provide robust incentives, while social-standing models are not informationally robust. Here we provide a model of indirect reciprocity based on simple, decentralized records: Each individual's record depends on the individual's own past behavior alone, and not on the individual's partners' past behavior or their partners' partners' past behavior. When social dilemmas exhibit a coordination motive (or strategic complementarity), tolerant trigger strategies based on simple records can robustly support positive social cooperation and exhibit strong stability properties. In the opposite case of strategic substitutability, positive social cooperation cannot be robustly supported. Thus, the strength of short-run coordination motives in social dilemmas determines the prospects for robust long-run cooperation.

A second-order stability analysis for the continuous model of indirect reciprocity.

Reputation is one of key mechanisms to maintain human cooperation, but its analysis gets complicated if we consider the possibility that reputation does not reach consensus because of erroneous assessment. The difficulty is alleviated if we assume that reputation and cooperation do not take binary values but have continuous spectra so that disagreement over reputation can be analysed in a perturbative way. In this work, we carry out the analysis by expanding the dynamics of reputation to the second order of perturbation under the assumption that everyone initially cooperates with good reputation. The second-order theory clarifies the difference between Image Scoring and Simple Standing in that punishment for defection against a well-reputed player should be regarded as good for maintaining cooperation. Moreover, comparison among the leading eight shows that the stabilizing effect of justified punishment weakens if cooperation between two ill-reputed players is regarded as bad. Our analysis thus explains how Simple Standing achieves a high level of stability by permitting justified punishment and also by disregarding irrelevant information in assessing cooperation. This observation suggests which factors affect the stability of a social norm when reputation can be perturbed by noise.

Indirect reciprocity with private, noisy, and incomplete information.

Indirect reciprocity is a mechanism for cooperation based on shared moral systems and individual reputations. It assumes that members of a community routinely observe and assess each other and that they use this information to decide who is good or bad, and who deserves cooperation. When information is transmitted publicly, such that all community members agree on each other's reputation, previous research has highlighted eight crucial moral systems. These "leading-eight" strategies can maintain cooperation and resist invasion by defectors. However, in real populations individuals often hold their own private views of others. Once two individuals disagree about their opinion of some third party, they may also see its subsequent actions in a different light. Their opinions may further diverge over time. Herein, we explore indirect reciprocity when information transmission is private and noisy. We find that in the presence of perception errors, most leading-eight strategies cease to be stable. Even if a leading-eight strategy evolves, cooperation rates may drop considerably when errors are common. Our research highlights the role of reliable information and synchronized reputations to maintain stable moral systems.

Dynamic effects of enforcement on cooperation.

In situations where social payoffs are not aligned with private incentives, enforcement with fines can be a way to sustain cooperation. In this paper we show, by the means of a laboratory experiment, that past fines can have an effect on current behavior even when no longer in force. We document two mechanisms: (i) Past fines affect directly individuals' future propensity to cooperate, and (ii) when fines for noncooperation are in place in the past, individuals experience higher levels of cooperation from partners and, consistent with indirect reciprocity motives, are in turn nicer toward others once these fines have been removed. This second mechanism is empirically prevalent and, in contrast with the first one, induces a snowball effect of past enforcement. Our results can inform the design of costly enforcement policies.

Genetic and Environmental Structure of Altruism Characterized by Recipients in Relation to Personality.

Background and Objectives: Altruism is a form of prosocial behavior with the goal of increasing the fitness of another individual as a recipient while reducing the fitness of the actor. Although there are many studies on its heterogeneity, only a few behavioral genetic studies have been conducted to examine different recipient types: family members favored by kin selection, the dynamic network of friends and acquaintances as direct reciprocity, and strangers as indirect reciprocity. Materials and Methods: This study investigated the genetic and environmental structure of altruism with reference to recipient types measured by the self-report altruism scale distinguished by the recipient (the SRAS-DR) and examine the relationship to personality dimensions measured by the NEO-FFI with a sample of 461 adult Japanese twin pairs. Results: The present study shows that there is a single common factor of altruism: additive genetic effects explain 51% of altruism without a shared environmental contribution. The genetic contribution of this single common factor is explained by the genetic factors of neuroticism (N), extraversion (E), openness to experience (O), and conscientiousness (C), as well as a common genetic factor specific to altruism. Only altruism toward strangers is affected by shared environmental factors. Conclusions: Different types of altruistic personality are constructed by specific combinational profiles of general personality traits such as the Big Five as well as a genetic factor specific to altruism in each specific way.

Paying it back and forward: The impact of experiencing and observing others' sharing and stinginess on preschoolers' own sharing behavior and expectations.

Recent research suggests that children's sharing behavior is affected by experiencing or observing others' sharing. These effects have been studied within research on the development of reciprocity and the effects of social modeling. In the current study, direct and indirect types of reciprocity and social modeling were assessed in 3- to 6-year-old children in three experiments (overall N = 382). In each experiment, we explored whether negative and positive social behavior were similarly paid back and forward in each of the different types of reciprocity. Moreover, we assessed the extent to which children reciprocated toward the protagonist who had performed the actual behavior and toward a neutral other. In Experiment 1, children experienced another's sharing behavior as recipients and could then allocate resources to this character and a neutral other. In Experiment 2, children observed another's sharing behavior and could then allocate resources to this character and a neutral other. In Experiment 3, children were asked to predict another protagonist's sharing in the same context as in Experiment 1. Overall, children treated the protagonist and the neutral other similarly and predicted others to do the same. Yet, they were more likely to reciprocate negative acts in indirect types of reciprocity. The results are interpreted with respect to the impact of observational learning and representational development on children's social behavior.

Adolescent indirect reciprocity: Evidence from incentivized economic paradigms.

INTRODUCTION: Indirect reciprocity serves as a crucial component of how we interact with strangers. Two types of indirect reciprocity can be distinguished: pay-it-forward reciprocity and third party reciprocity. Pay-it-forward reciprocity refers to behaviors where people who have been treated well by others (either fairly or generously), extend that fairness or generosity to a stranger. Third-party reciprocity refers to behaviors where third-party bystanders altruistically punish those who transgress against others or kindly help the victims. The expansion of adolescents' social world increases opportunities to exercise indirect reciprocity yet very little research has focused on this topic in this age group. The current research addresses this lacuna and investigates how younger adolescents differ from older adolescents in pay-it-forward and third party reciprocity. METHODS: With incentivized economic paradigms, we investigated both types of indirect reciprocity in younger (n = 50) and older adolescents (n = 46). RESULTS: The pay-it-forward task revealed that receiving an equal (vs. unequal) distribution led both younger and older adolescents to become fairer to a third person. In the third-party task, older adolescents were more likely to devote their own resources to enforce fairness norms than younger adolescents. CONCLUSION: Our results shed light on how adolescents perceive and act in complex social settings where direct reciprocity is unrealistic. Both younger and older adolescents are capable of engaging in both forms of indirect reciprocity with older adolescents being more discriminative in their norm-enforcing behaviors.

Personal trust extends cooperation beyond trustees: A Mexican study.

We studied 2 groups of workers from Oaxaca (Mexico) with different levels of income and education to investigate the role that the affective-based psychological mechanism of personal trust, as evolutionarily acquired, plays on group cooperation. We measured trust levels through some questionnaires and cooperative behaviour through an iterated prisoner's dilemma under different conditions and analysed trust networks of group members. While these groups did not differ in trust levels or cooperation among trustees, they did differ in terms of cooperation with other group members. Such differences are related to dissimilarities in the trust network topology-as a measure of group cohesion. These results suggest that some personal trust networks extend cooperation within a group beyond trustees in a way that complements the role of the reputation for indirect reciprocity.

The emergence and selection of reputation systems that drive cooperative behaviour.

Reputational concerns are believed to play a crucial role in explaining cooperative behaviour among non-kin humans. Individuals cooperate to avoid a negative social image, if being branded as defector reduces pay-offs from future interactions. Similarly, individuals sanction defectors to gain a reputation as punisher, prompting future co-players to cooperate. But reputation can only effectively support cooperation if a sufficient number of individuals condition their strategies on their co-players' reputation, and if a sufficient number of group members are willing to record and transmit the relevant information about past actions. Using computer simulations, this paper argues that starting from a pool of non-cooperative individuals, a reputation system based on punishment is likely to emerge and to be the driver of the initial evolution of cooperative behaviour. However, once cooperation is established in a group, it will be sustained mainly through a reputation mechanism based on cooperative actions.

Does observability affect prosociality?

The observation of behaviour is a key theoretical parameter underlying a number of models of prosociality. However, the empirical findings showing the effect of observability on prosociality are mixed. In this meta-analysis, we explore the boundary conditions that may account for this variability, by exploring key theoretical and methodological moderators of this link. We identified 117 papers yielding 134 study level effects (total n = 788 164) and found a small but statistically significant, positive association between observability and prosociality (r = 0.141, 95% confidence interval = 0.106, 0.175). Moderator analysis showed that observability produced stronger effects on prosociality: (i) in the presence of passive observers (i.e. people whose role was to only observe participants) versus perceptions of being watched, (ii) when participants' decisions were consequential (versus non-consequential), (iii) when the studies were performed in the laboratory (as opposed to in the field/online), (iv) when the studies used repeated measures (instead of single games), and (v) when the studies involved social dilemmas (instead of bargaining games). These effects show the conditions under which observability effects on prosociality will be maximally observed. We describe the theoretical and practical significance of these results.

A solution for private assessment in indirect reciprocity using solitary observation.

Although indirect reciprocity is a fundamental mechanism in the evolution of human cooperation, most studies assume public assessment in which individuals are not permitted to obtain private assessments of others. Existing studies on private assessment have used individual-based simulations because of the analytical difficulty involved. Here, we develop an analytical method using solitary observation to solve private assessment in indirect reciprocity problem without any approximation. In this study, we formulate a model of solitary observation and calculate the replicator dynamics systems of five leading norms of indirect reciprocity. Indirect reciprocity in private assessment provides a different result to that in public assessment. According to the existence proofs of cooperative evolutionarily stable (CES) points in the system, strict norms (stern judging and shunning) have no CES point in private assessment, while they do in public assessment. Image scoring does not change the system regardless of the assessment types because it does not use second-order information. In tolerant norms (simple standing and staying), the CES points move to co-existence of norms and unconditional cooperators. Despite the fact that there is no central coercive assessment system in private assessment, the average cooperation rate at the CES points in private assessment is greater than that in public assessment. This is because private assessment gives unconditional cooperators a role. Our results also show the superiority of the staying norm. Compared with simple standing, staying has three advantages in private assessment: a higher cooperation rate, easiness of invasion into defectors, and robustness to maintain cooperative evolutionarily stable situations. Our results are applicable to general social dilemmas in relation to private information. Under some dilemmas, norms or assessment rules should be carefully chosen to enable cooperation to evolve.