Indirect Reciprocity Research Articles

Exact cluster dynamics of indirect reciprocity in complete graphs

Exact cluster dynamics of indirect reciprocity in complete graphs

Clarifying social norms which have robustness against reputation costs and defector invasion in indirect reciprocity

The evolution of cooperation through indirect reciprocity is a pivotal mechanism for sustaining large-scale societies. Because third parties return cooperative behaviour in indirect reciprocity, reputations that assess and share these third parties’ behaviour play an essential role. Studies on indirect reciprocity have predominantly focused on the costs associated with cooperative behaviour, overlooking the costs tied to the mechanisms underpinning reputation sharing. Here, we explore the robustness of social norms necessary to secure the stability of indirect reciprocity, considering both the costs of reputation and the resilience against perfect defectors. Firstly, our results replicate that only eight social norms, known as the ‘leading eight,’ can establish a cooperative regime. Secondly, we reveal the robustness of these norms against reputation costs and perfect defectors. Our analysis identifies four norms that exhibit resilience in the presence of defectors due to their neutral stance on justified defection and another four that demonstrate robustness against reputation costs through their negative evaluation of unjustified cooperation. The study underscores the need to further research how reputational information is shared within societies to promote cooperation in diverse and complex environments.

Render help or stand by? The effect of group size on third-party punishment and its neural mechanisms

Third-party punishment (TPP) is the punishment that an individual executes on a violator as a third party or observer to maintain social norms. Many studies have provided insights into the neural mechanisms of third-party punishment in group environments. Still, only some studies have focused on the neural mechanisms of third-party punishment in different group sizes. This study used EEG analysis to explore the effects of group size on third-party punishment and its neural activity characteristics from the context of gain and loss. The results show that the punishment rate and amount of the third party in the small group size and loss context were significantly higher than that in the large group size and gain context. EEG results showed that third-party punishment in small groups induced greater P2 than in large groups. In the loss context, the third-party punishment in the large group size induced more negative LNP and activated more theta band activation than in the small group. The results showed that the motivation of the third party to seek a positive reputation in the small size exceeds the balance of its economic interests and tends to punish the violator for maintaining fair norms. The loss context plays a promoting role in this process. However, in the large size, the third-party consideration of its interests was stronger than the willingness to maintain social norms. This study provided neuroscientific evidence for third-party punishment to maintain fair norms in a group environment and further explanations from neuroscience for understanding Indirect Reciprocity Theory.

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.

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.

Intergenerational Cooperation and Justice between Age Groups

In this paper, I bring together the problems of justice between age groups and intergenerational cooperation in light of real-life demographic trends. I begin by presenting a simple model of intergenerational cooperation based on indirect reciprocity and show how cooperation can break down due to exogenous factors, including demographic change. I use the model to make the argument that principles for justice between age groups must be sensitive to the stability of intergenerational cooperation. I illustrate my thesis by considering the debate between distributive and relational egalitarians on justice between age groups.

Group-bounded indirect reciprocity and intergroup gossip

Gossip, the exchange of information about absent others, is ingrained in the system of indirect reciprocity, in which participating members selectively interact and cooperate with others with a good reputation. Previous psychological theorizing suggests that indirect reciprocity is perceived to be bounded by group membership. We aimed to examine whether the group-bounded indirect reciprocity perspective explains intergroup gossip. We thus explored how group membership shapes the expectations about how gossip is used and willingness to gossip within and across group boundaries. We conducted three studies (total N = 986) and re-analyzed a published dataset (N = 690) and comprehensively investigated how willing people expect others to be to engage in within- and between-group gossip as well as how willing they themselves are to engage in both types of gossip, in minimal and university contexts. We found that consistent with the group-bounded indirect reciprocity perspective, people expected within group gossip to be more likely than intergroup gossip. In addition, in the minimal group context, we found that people were, in general, more willing to gossip towards in-group members rather than out-group members. However, in the university context, they were more willing to gossip about in-group and out-group members towards out-group and in-group members, respectively, suggesting that people may utilize intergroup gossip for strategic reasons. Our research was the first to experimentally elucidate the role of group membership in shaping expectations about gossip and willingness to gossip, and offers a promising starting point for future work on intergroup gossip and indirect reciprocity.

Who is a Leader in the Leading Eight? Indirect Reciprocity under Private Assessment

Indirect reciprocity is a mechanism that explains large-scale cooperation in human societies. In indirect reciprocity, an individual chooses whether to cooperate with another based on reputation information, and others evaluate the action as good or bad. Under what evaluation rule (called “social norm”) cooperation evolves has long been of central interest in the literature. It has been reported that if individuals can share their evaluations (i.e., public reputation), social norms called “leading eight” can be evolutionarily stable. On the other hand, when they cannot share their evaluations (i.e., private assessment), the evolutionary stability of cooperation is still in question. To tackle this question, we create a novel method to analyze the reputation structure in the population under private assessment. Specifically, we characterize each individual by two variables, “goodness” (what proportion of the population considers the individual as good) and “self-reputation” (whether an individual thinks of him or herself as good or bad), and analyze the stochastic process of how these two variables change over time. We discuss the evolutionary stability of each of the leading-eight social norms by studying the robustness against invasions of unconditional cooperators and defectors. We identify key pivots in those social norms for establishing a high level of cooperation or stable cooperation against mutants. Our finding gives an insight into how human cooperation is established in a real-world society. Published by the American Physical Society 2024

Evolutionary dynamics of direct and indirect reciprocity on networked populations

Direct, indirect and network reciprocity are key mechanisms fostering cooperation in societies. Though intrinsically interrelated, they are often studied separately. Unravelling the evolutionary dynamics of reciprocity in structured populations remains challenging. Here, we develop a general model to explore the evolution of direct and indirect reciprocity on networks. Drawing on our model, we derive a simple rule for cooperation to evolve through reciprocity. Applying this rule to 1 million random networks, we investigate how network topology influences evolutionary outcomes. We find that, in general, direct reciprocity is easier to promote cooperation on these networks. Additionally, direct reciprocity remains robust when a population adapts to the environment through social learning. Notably, environmental fluctuations significantly lower the threshold for cooperation through indirect reciprocity. Overall, our work sheds light on a fresh framework for comprehending the evolution of reciprocity.

INVITED PAPER: EMOTION EXPRESSION AND INDIRECT RECIPROCITY

This study explores how emotion expression (EE) can help promote positive indirect reciprocity while also breaking chains of negative indirect reciprocity. We report data from a two-stage dictator game and compare the decisions subjects make towards a third party both with and without the chance to express emotion. Standard economic models suggest opportunities to express emotion should have no impact on behavior. In sharp contrast to these predictions, we find that subjects who are treated unkindly behave more generously towards others in subsequent interactions if they have the opportunity to convey their emotions to a third party. Our findings have important welfare implications. In particular, they suggest that opportunities to express emotion can break negative reciprocity chains and promote generosity and social well-being even among those who have not themselves been previously well-treated. We argue that reference-dependent valuations can help to explain our results.

Evidence of direct and indirect reciprocity in network-structured economic games

Formal theoretical models propose that cooperative networks can be maintained when individuals condition behavior on social standing. Here, we empirically examine the predictions of such models of positive and negative indirect reciprocity using a suite of network-structured economic games in four rural Colombian communities (Nind = 496 individuals, Nobs = 53,876 ratings/transfers). We observe that, at a dyadic-level, individuals have a strong tendency to exploit and punish others in bad standing (e.g., those perceived as selfish), and allocate resources to those in good standing (e.g., those perceived as generous). These dyadic findings scale to a more generalized, community level, where reputations for being generous are associated with receipt of allocations, and reputations for being selfish are associated with receipt of punishment. These empirical results illustrate the roles that both positive and negative reciprocity, and costly punishment, play in sustaining community-wide cooperation networks.

Indirect reciprocity in Japanese

I shall discuss a special usage of the Japanese reciprocal expression otagai. In this usage, otagai does not occur as the object of a transitive verb and does not induce a reciprocal interpretation. Rather, it seems to modify the nominal in the subject position. I argue that otagai in such examples expresses reciprocity only indirectly in that the relation is not expressed overtly in the sentence in question. The relation is a psychological one in that the sentence as a whole says that each participant of the speech context knows that the other participant(s) have the property given by the overt predicate in the sentence. This, then, entails that each of them has this same property since know is a factive predicate. Since each participant has to be in a position to assess what the other member(s) are thinking of, the group of people in question must know each other well. This means that the nature of reciprocity is essentially the same in English and Japanese except that otagai could introduce a covert psychological relation to satisfy the reciprocity requirement. The article also discusses the similarity between the indirect use of otagai and the indirect passive in Japanese.

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.

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.

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.

Community membership and reciprocity in lending: Evidence from informal markets

We study credit access in informal economies where market institutions, such as financial reporting systems, auditing, and courts, are nonexistent or function poorly. Using the setting of a large bazaar in India, we find that community membership plays a vital role in access to credit. Wholesalers are more likely to provide credit and offer greater amounts of credit to within-community retailers, and are more lenient when these retailers are delinquent. Furthermore, wholesalers who lent preferentially to their community retailers pre-COVID are more likely to receive help from their community following the COVID-19–related income shock, particularly from same-community landlords and suppliers. Also, wholesalers with low endowments, those with greater within-community information flow about them, and those facing income shocks are more likely to provide preferential credit to their community retailers. Our findings are consistent with an indirect reciprocity mechanism explaining within-community credit flows.

The Evolution of Cooperation and Diversity under Integrated Indirect Reciprocity

The Evolution of Cooperation and Diversity under Integrated Indirect Reciprocity

Why Neighbors Would Help: A Vignette Experiment on Reciprocity in Informal Helping

Reciprocity in informal helping, or informal volunteering, is often seen as a way to ensure that people who are not altruistically motivated exchange help. Yet, it could be problematic for those who are unable to help, as they would be excluded from this exchange. We study to what extent people’s reciprocity expectations affect informal helping intentions and whether necessity of helping and perceived helpfulness (indirect reciprocity) compensate and moderate this relationship. Expectations are tested with a factorial survey conducted among the Longitudinal Internet studies for the Social Sciences panel ( N vignettes = 3,299). Multilevel regression analyses show that people have stronger intentions to help those who are likely to reciprocate but that a strong need for help and having helped others in the past are more important reasons to help. Furthermore, the effect of likelihood of reciprocity on informal helping intentions is stronger for neighbors who never helped others. Policy implications of these results are discussed.

Psychological mechanisms underlying ingroup favouritism in cooperation: Revisiting the reputation management and expectation hypotheses

According to the theory of bounded generalized reciprocity (BGR), intergroup contexts afford individuals the assumption that indirect reciprocity is bounded by group membership, and this shapes ingroup favouritism in cooperation. The assumption of bounded indirect reciprocity is hypothesized to result in ingroup favouritisms via two pathways: it leads people to behave in ways that earn and maintain a positive reputation in the eyes of ingroup, but not outgroup, members (the reputation management hypothesis), and it leads individuals to expect other ingroup members to be more cooperative than outgroup members (the expectation hypothesis). In other words, BGR offers two parallel psychological explanations for why people display ingroup favouritism. While the latter hypothesis has gained much experimental support, evidence for the former is rather scarce. Here, we report a direct test of both the reputation management hypothesis and the expectation hypothesis using two economic games. Overall, we found support for the expectation hypothesis, but not for the reputation management hypothesis.