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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.

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.

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.

Humans have achieved widespread cooperation, largely sustained by mechanisms such as indirect reciprocity, which relies on reputation and social norms. People are highly motivated to maintain a good reputation, and social norms play a critical role in reputation systems by defining acceptable behavior, helping prevent exploitation by free-riders. However, there is a gap between theory and experiment in handling reputation information, with experiments often failing to capture the complexity that theoretical models propose. Here, we address two key issues: what kind of information is needed to define reputation as a social norm and the appropriate level of granularity required for reputation information to function effectively. This paper combines scenario-based experiments and evolutionary game theory to investigate the social norms individuals adopt in real-world settings, aiming to uncover the stability of these norms. Our results show that reputations should be categorized into three levels good, neutral, and bad. Results suggest gradual reputation dynamics that increase and decrease gradually due to cooperation or defection. However, a person’s reputation remains unchanged only when they defect against a bad reputation. Our experimental and theoretical results support critical insights into the dynamics of reputation and social norms within indirect reciprocity, challenging traditional binary reputational evaluations. The gradual nature of reputation updating and the use of nuanced evaluations provide a more realistic model of reputation dynamics.

Human cooperation relies on both direct and indirect reciprocity. While these mechanisms are often treated as separate, real-world decision-making frequently involves integrating the two. However, the existing literature has paid limited attention to the contextual factors and mechanisms supporting the coexistence of direct and indirect reciprocity. This study proposes and analyses a model of integrated reciprocity that combines personal experiences with reputational information. Using agent-based simulations, we systematically and comprehensively evaluate social norms and demonstrate that tolerant integrated reciprocity, which incorporates a partner’s past behaviour and reputation, can sustain cooperation more robustly than strategies based solely on direct or indirect reciprocity. In particular, the combination of tolerant integrated reciprocity with the “Standing” norm maintains high cooperation levels even in noisy environments characterised by assessment and implementation errors. These findings suggest that tolerance and using multiple information sources provide an adaptive advantage in sustaining cooperation.

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.

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.

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.

Economists have investigated how price–wage rigidity influences macroeconomic stability. A widely accepted view asserts that increased rigidity destabilizes an economy by requiring a larger quantity adjustment. In contrast, the Old Keynesian view regards nominal rigidity as a stabilizing factor, because it reduces fluctuations in income and thus aggregate demand. To examine whether price–wage stickiness is stabilizing or destabilizing, we build an agent-based Wicksell–Keynes macroeconomic model, which is completely closed and absolutely free from any external shocks, including policy interventions. In the model, firms setting prices and wages make both employment and investment decisions under demand constraints, while a fractional-reserve banking sector sets the interest rate and provides the firms with investment funds. As investment involves a gestation period, it is conducive to overproduction, thereby causing alternate seller’s and buyer’s markets. In the baseline simulation, a stable economy emerges with short-run business cycles and long-run fluctuations. One unique feature of the economy is its remarkable resilience: When afflicted by persistent deflation, it often manages to reverse the deflationary spiral and get back on a growth track, ultimately achieving full or nearly full employment. The virtual experiments demonstrate that prices and wages must both be moderately rigid to ensure long-run stability. The key stabilizing mechanism is a recurring demand-sufficient economy, in which firms are allowed to increase employment while simultaneously cutting real wages.

Many practitioners as well as researchers explore promoting environmentally conscious behavior in the context of public goods systems. Numerous experimental studies revealed various types of incentives to increase cooperation on public goods. There is ample evidence that monetary and non-monetary incentives, such as donations, have a positive effect on cooperation in public goods games that exceeds fully rational and optimal economic decision making. Despite an accumulation of these studies, in the typical setting of these experiments participants decide on an allocation of resources to a public pool, but they never exert actual effort. However, in reality, we often observe that players’ real effort is required in these public goods game situations. Therefore, more analysis is needed to draw conclusions for a wider set of incentive possibilities in situations similar to yet deviating from resource allocation games. Here we construct a real effort public goods game in an online experiment and statistically analyze the effect different types of incentives have on cooperation. In our experiment, we examine combinations of monetary and social incentives in a setting aimed closer to practical realities, such as financial costs and real effort forming part of the decision to cooperate on a public good. In our real effort public goods game participants cooperate and defect on image-scoring tasks. We find that in our setting economic and social incentives produce an asymmetric effect. Interestingly economic incentives decreased the share of highly uncooperative participants, while social incentives raised the share of highly cooperative participants.