A norm knockout method on indirect reciprocity to reveal indispensable 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.

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.

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.

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'.

Adherence to public institutions that foster cooperation

Humans typically consider altruism a moral good and condition their social behavior on the moral reputations of others. Indirect reciprocity explains how social norms and reputations support cooperation: individuals cooperate with others who are considered good. Indirect reciprocity works when an institution monitors and publicly broadcasts moral reputations. Here we develop a theory of adherence to public monitoring in societies where individuals are, at first, independently responsible for evaluating the reputations of their peers. Using a mathematical model, we show that adherence to an institution of moral assessment can evolve and promote cooperation under four different social norms, including norms that previous studies found to perform poorly. We determine how an institution's size and its degree of tolerance towards anti-social behavior affect the rate of cooperation. Public monitoring serves to eliminate disagreements about reputations, which increases cooperation and payoffs, so that adherence evolves by social contagion and remains robust against displacement.

A Review of Theoretical Studies on Indirect Reciprocity

Despite the accumulation of research on indirect reciprocity over the past 30 years and the publication of over 100,000 related papers, there are still many issues to be addressed. Here, we look back on the research that has been done on indirect reciprocity and identify the issues that have been resolved and the ones that remain to be resolved. This manuscript introduces indirect reciprocity in the context of the evolution of cooperation, basic models of social dilemma situations, the path taken in the elaboration of mathematical analysis using evolutionary game theory, the discovery of image scoring norms, and the breakthroughs brought about by the analysis of the evolutionary instability of the norms. Moreover, it presents key results obtained by refining the assessment function, resolving the punishment dilemma, and presenting a complete solution to the social dilemma problem. Finally, it discusses the application of indirect reciprocity in various disciplines.

Justified defection is neither justified nor unjustified in indirect reciprocity

Indirect reciprocity is one of the major mechanisms in the evolution of human cooperation. In indirect reciprocity, social norms with which individuals distinguish good people from bad people play essential roles. Despite extensive studies on the evolution of cooperation in indirect reciprocity, little is known about which social norms people actually adopt. Here we reveal what kind of norms are adopted by people in indirect reciprocal situations in daily life by using scenario-based experiments. The results showed that people evaluated "justified defection" as neither good nor bad and withheld their evaluation. Theoretically, social norms that evaluate justified defection as good are required for cooperation to be stable. However, the norm that people actually adopted deviates from the theoretical predictions. Our results indicate the necessity to reconsider the justification of "justified defection" in the evolution of cooperation.

Effect of voluntary participation on an alternating and a simultaneous prisoner's dilemma

We studied the evolution of cooperation in the framework of evolutionary game theory, implementing voluntary participation in the prisoner's dilemma. Although previous studies have tried to overcome the dilemma by introducing voluntary participation called a "loner," the question of which strategies among various strategies including voluntary participation are adaptive under competitive circumstances is still an unsolved puzzle. Here we have developed a model that consists of all possible strategies using a one-period memory of past actions. This model enables us to analyze a "melting pot" of strategies, wherein several strategies interact and compete with each other. Our results revealed that one strategy, in which one escapes if a partner defects or cooperates if a partner becomes a loner, dominates and maintains cooperation in an alternating prisoner's dilemma game. However, the so-called "win-stay, lose-shift" strategy dominates in a simultaneous prisoner's dilemma game. Our simulations clearly show that voluntary participation in the prisoner's dilemma game works in the alternating situation rather than the simultaneous one.

Evolution of empathetic moral evaluation

Social norms can promote cooperation by assigning reputations to individuals based on their past actions. A good reputation indicates that an individual is likely to reciprocate. A large body of research has established norms of moral assessment that promote cooperation, assuming reputations are objective. But without a centralized institution to provide objective evaluation, opinions about an individual’s reputation may differ across a population. In this setting we study the role of empathy–the capacity to form moral evaluations from another person’s perspective. We show that empathy tends to foster cooperation by reducing the rate of unjustified defection. The norms of moral evaluation previously considered most socially beneficial depend on high levels of empathy, whereas different norms maximize social welfare in populations incapable of empathy. Finally, we show that empathy itself can evolve through social contagion. We conclude that a capacity for empathy is a key component for sustaining cooperation in societies.

When meerkats have pups, they employ an individual to stand guard and warn the others of potential dangers and predators, putting their own life at risk. What seems like a selfless act is actually a common behavior found throughout the animal kingdom. But rather than acting out of concern for another ones wellbeing, it is considered to be an altruistic behavior towards kin, where an individual sacrifices its own reproductive success for the sake of the reproductive fitness of its entire clan.

In human societies, however, people often act altruistically towards unrelated individuals and have developed sophisticated systems of moral evaluation to decide who is worthy of cooperation and likely to reciprocate a favor. In other words, individuals will only help those who have a good reputation for being altruistic themselves. However, for this system to work, reputations need to be public knowledge, and societies need to agree on everyones reputations. But what happens when opinions about an individual's reputation are private and vary across a population?

Now, Radzvilavicius et al. wanted to find out whether altruism can emerge when people have different opinions about each others moral reputations. To do so, they used a so-called evolutionary game theory a mathematical description of how strategies change in a population over time. In their model, each individual could decide if they wanted to pay a personal cost to create a benefit for another individual. Each participant decided whether to act altruistically based on the reputation of the recipient; observers could update the individuals reputation based on their behavior.

The mathematical model revealed that when people are more empathetic and able to put themselves in someone elses shoes, altruism tends to spread over time. When people take into account different opinions and form moral judgements from another person's perspective, the population can sustain a higher level of cooperation. Moreover, the capacity for taking another person's perspective can itself evolve and remain stable in a population meaning that those individuals who evaluate each other empathetically tend to do better, and empathy spreads through social influence.

These findings can help us understand how empathy might have evolved in societies that value reputation as a means of reciprocity. A next step could be to test the theory developed by Radzvilavicius et al. in manipulative experiments, or to compare the theory to field data on reputations and behavior in online interactions.

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.