Indirect reciprocity can overcome free-rider problems on costly moral assessment

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'.

Two ways to overcome the three social dilemmas of indirect reciprocity

Indirect reciprocity is one of the main principles of evolving cooperation in a social dilemma situation. In reciprocity, a positive score is given to cooperative behaviour while a negative score is given to non-cooperative behaviour, and the dilemma is resolved by selectively cooperating only with those with positive scores. However, many studies have shown that non-cooperation with those who have not cooperated also downgrades one's reputation; they have called this situation the scoring dilemma. To address this dilemma, the notion of justified punishments has been considered. The notion of justified punishment allows good individuals who defect against bad co-players to keep their standing. Despite numerous studies on justified punishment, it is unknown whether this solution leads to a new type of dilemma because reputations may be downgraded when the intent of punishment is not correctly communicated. The dilemma of punishment has so far been rarely analysed, and thus, the complete solution of the mechanism for evolving cooperation using the principle of indirect reciprocity has not been found yet. Here, we identify sufficient conditions to overcome each of the three dilemmas including the dilemma of punishment to maintain stable cooperation by using the framework of evolutionary game theory. This condition includes the principle of detecting free riders, which resolves the social dilemma, the principle of justification, which resolves the scoring dilemma, and the principle of generosity, which resolves the dilemma of punishment. A norm that satisfies these principles can stably maintain social cooperation. Our insights may offer a general assessment principle that applies to a wide range of subjects, from individual actions to national decisions.

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.

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.

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.

Tolerant indirect reciprocity can boost social welfare through solidarity with unconditional cooperators in private monitoring

Indirect reciprocity is an important mechanism for resolving social dilemmas. Previous studies explore several types of assessment rules that are evolutionarily stable for keeping cooperation regimes. However, little is known about the effects of private information on social systems. Most indirect reciprocity studies assume public monitoring in which individuals share a single assessment for each individual. Here, we consider a private monitoring system that loosens such an unnatural assumption. We explore the stable norms in the private system using an individual-based simulation. We have three main findings. First, narrow and unstable cooperation: cooperation in private monitoring becomes unstable and the restricted norms cannot maintain cooperative regimes while they can in public monitoring. Second, stable coexistence of discriminators and unconditional cooperators: under private monitoring, unconditional cooperation can play a role in keeping a high level of cooperation in tolerant norm situations. Finally, Pareto improvement: private monitoring can achieve a higher cooperation rate than does public monitoring.

The evolution of conditional moral assessment in indirect reciprocity

Indirect reciprocity is a major mechanism in the maintenance of cooperation among unrelated individuals. Indirect reciprocity leads to conditional cooperation according to social norms that discriminate the good (those who deserve to be rewarded with help) and the bad (those who should be punished by refusal of help). Despite intensive research, however, there is no definitive consensus on what social norms best promote cooperation through indirect reciprocity, and it remains unclear even how those who refuse to help the bad should be assessed. Here, we propose a new simple norm called “Staying” that prescribes abstaining from assessment. Under the Staying norm, the image of the person who makes the decision to give help stays the same as in the last assessment if the person on the receiving end has a bad image. In this case, the choice about whether or not to give help to the potential receiver does not affect the image of the potential giver. We analyze the Staying norm in terms of evolutionary game theory and demonstrate that Staying is most effective in establishing cooperation compared to the prevailing social norms, which rely on constant monitoring and unconditional assessment. The application of Staying suggests that the strict application of moral judgment is limited.

Evolution of cooperation under indirect reciprocity and arbitrary exploration rates

Cooperation has been recognized as an evolutionary puzzle since Darwin, and remains identified as one of the biggest challenges of the XXIst century. Indirect Reciprocity (IR), a key mechanism that humans employ to cooperate with each other, establishes that individual behaviour depends on reputations, which in turn evolve depending on social norms that classify behaviours as good or bad. While it is well known that different social norms give rise to distinct cooperation levels, it remains unclear how the performance of each norm is influenced by the random exploration of new behaviours, often a key component of social dynamics where a plethora of stimuli may compel individuals to deviate from pre-defined behaviours. Here we study, for the first time, the impact of varying degrees of exploration rates - the likelihood of spontaneously adopting another strategy, akin to a mutation probability in evolutionary dynamics - in the emergence of cooperation under IR. We show that high exploration rates may either improve or harm cooperation, depending on the underlying social norm at work. Regarding some of the most popular social norms studied to date, we find that cooperation under Simple-standing and Image-score is enhanced by high exploration rates, whereas the opposite occurs for Stern-judging and Shunning.