Indirect reciprocity in three types of social dilemmas

Indirect reciprocity, in which individuals help others with a good reputation but not those with a bad reputation, is a mechanism for cooperation in social dilemma situations when individuals do not repeatedly interact with the same partners. In a relatively large society where indirect reciprocity is relevant, individuals may not know each other's reputation even indirectly. Previous studies investigated the situations where individuals playing the game have to determine the action possibly without knowing others' reputations. Nevertheless, the possibility that observers of the game, who generate the reputation of the interacting players, assign reputations without complete information about them has been neglected. Because an individual acts as an interacting player and as an observer on different occasions if indirect reciprocity is endogenously sustained in a society, the incompleteness of information may affect either role. We examine the game of indirect reciprocity when the reputations of players are not necessarily known to observers and to interacting players. We find that the trustful discriminator, which cooperates with good and unknown players and defects against bad players, realizes cooperative societies under seven social norms. Among the seven social norms, three of the four suspicious norms under which cooperation (defection) to unknown players leads to a good (bad) reputation enable cooperation down to a relatively small observation probability. In contrast, the three trustful norms under which both cooperation and defection to unknown players lead to a good reputation are relatively efficient.

We consider a spatial generalization of evolutionary game theory in which strategies are distributed over a spatial array of sites. We assume that the strategy corresponding to a given site has local interactions with the strategies sitting on neighbouring sites, and that the strategies change if neighbouring strategies are doing better. After briefly setting the stage with a formal definition of spatial evolutionary game theory, we consider the spatial extension of the Hawk-Dove game, and we show that the results are qualitatively different from those obtained from classical evolutionary game theory. For example, the proportion of Hawks in the population is in general lower in the spatial game than in the classical one. We also consider spatial generalizations of the extensions of the Hawk-Dove game obtained by including strategies such as Retaliator and Bully. Here, too, the results from the spatial game are very different from the classical results. In particular, with space Retaliator is a much more successful strategy than one would expect from classical considerations. This suggests that, in general, spatial structure may facilitate the evolution of strategies such as Retaliator, which do not necessarily prosper classically, and which are reminiscent of the \`nice', \`provokable' and `forgiving' strategies which seem to play a central role in the evolution of cooperation. The results indicate that including spatial structure in evolutionary game theory is a fruitful extension.

Greed and fear in multiperson social dilemmas

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.

Models of large-scale human cooperation take two forms. 'Indirect reciprocity' occurs when individuals help others in order to uphold a reputation and so be included in future cooperation. In 'collective action', individuals engage in costly behaviour that benefits the group as a whole. Although the evolution of indirect reciprocity is theoretically plausible, there is no consensus about how collective action evolves. Evidence suggests that punishing free riders can maintain cooperation, but why individuals should engage in costly punishment is unclear. Solutions to this 'second-order free rider problem' include meta-punishment, mutation, conformism, signalling and group-selection. The threat of exclusion from indirect reciprocity can sustain collective action in the laboratory. Here, we show that such exclusion is evolutionarily stable, providing an incentive to engage in costly cooperation, while avoiding the second-order free rider problem because punishers can withhold help from free riders without damaging their reputations. However, we also show that such a strategy cannot invade a population in which indirect reciprocity is not linked to collective action, thus leaving unexplained how collective action arises.

In order to examine the pragmatic methods of solving social dilemmas, it is important to understand the logical structure of dilemmas that underpin actual real-life problems. To this end, and also to facilitate the basic understanding of social dilemmas, the categories and types of representative social dilemmas will be reviewed in the following section.

Communication and collective action: language and the evolution of human cooperation

The purpose of this chapter is to show a new way to see social dilemmas and to explain people’s decision making in social dilemmas. The key concept in our analysis is social orientation. We will apply the social orientation analysis, as was done for 2×2 matrix games, to an analysis of decision making by people in social dilemmas. To do so, we will present new formulations for the two types of social dilemmas: “free rider” and “tragedy of the common.” Our analysis will show how our formulations are different from, interrelated with, and superior to the payoff matrix expression. Furthermore, we will also show how the two types of social dilemmas are different, how social dilemma situations are normalized, and how people’s decision making can be explained using a social orientation model.

Environmental heterogeneity unifies the effect of spatial structure on the altruistic cooperation in game-theory paradigms

How and why cooperation is able to prevail in social dilemma situations is an intensely investigated subject with much relevance for the well-being of human societies. Many mechanisms that promote cooperation have been identified within the theoretical framework of evolutionary game theory. Here, we advance the subject by relaxing the simplified assumption that each player in the population has the same number of interaction neighbors. This assumption indeed contradicts actual conditions, and it is, thus, important to understand what consequences this has for the evolution of cooperation. We therefore take into consideration that replacement and interaction neighbors can differ, and moreover, that each player can randomly select the number of interaction neighbors. The results of Monte Carlo simulations reveal that the introduction of neighborhood diversity elevates the level of cooperation in various types of social dilemmas, including the prisoner's dilemma and the snowdrift game. We also show that the same mechanism of cooperation promotion remains valid in evolutionary multigames. Taken together, our results strongly support the assertion that diversity, in general, is a strong facilitator of cooperation even under the most testing conditions and they provide a rationale for engineering better social systems.

Chaos, oscillation and the evolution of indirect reciprocity in n-person games

Erratum to “Indirect reciprocity in three types of social dilemmas” [J. Theor. Biol. 355 (2014) 117–127

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.

A tragedy of the commons, in which rational behavior of individuals to maximize their own payoffs depletes common resources, is one of the most important research topics in game theory. To better understand the social dilemma problem, recent studies have developed a theoretical framework of feedback-evolving game where individual behavior affects an environmental (renewable) resource and the environmental resource changes individual payoffs. While previous studies assumed that the frequency of defectors increases (prisoner's dilemma [PD] game) when the environmental resource is abundant to investigate an oscillating tragedy of the commons, it is also possible for other types of game to produce the social dilemma. In this paper, we extend the feedback-evolving game by considering not only PD game, but also the other three game structures when the environmental resource is replete for a reasonably complete classification. The three games are Chicken game where defectors and cooperators coexist through minority advantage, Stag-Hunt (SH) game with minority disadvantage, and Trivial game where the frequency of cooperators increases. In addition, we utilize a dilemma phase plane to visually track (transient) dynamics of game structure changes. We found that an emergent initial condition dependence (i.e. bistability) is pervasive in the feedback-evolving game when the three games are involved. We also showed that persistent oscillation dynamics arise even with Chicken or SH games in replete environments. Our generalized analysis will be an important step to further extend the theoretical framework of feedback-evolving game to various game situations with environmental feedback.

Indirect reciprocity is a key mechanism for the evolution of human cooperation. There are normally two choices in the standard model of indirect reciprocity which works through reputation. Here we introduced the role of costly punishment into the model. The players could have the third choice besides cooperation and defection. The dynamics of cooperation in indirect reciprocity is analyzed under the social norms which depend on the action of the donor and the reputation of the recipient. It is found that those strategies using costly punishment which allow the evolutionary stability of cooperation typically reduce the average payoff of the population and there is only a small parameter region where costly punishment is evolutionary stable and more efficient. The computer simulations based on agent in finite populations are performed and the result is agreement with our theoretical predictions.Keywordscostly punishmentindirect reciprocitydynamicsevolutionary stable strategysocial norm