Indirect reciprocity under incomplete observation

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.     

Indirect reciprocity and the evolution of “moral signals”

Signals regarding the behavior of others are an essential element of human moral systems and there are important evolutionary connections between language and large-scale cooperation. In particular, social communication may be required for the reputation tracking needed to stabilize indirect reciprocity. Additionally, scholars have suggested that the benefits of indirect reciprocity may have been important for the evolution of language and that social signals may have coevolved with large-scale cooperation. This paper investigates the possibility of such a coevolution. Using the tools of evolutionary game theory, we present a model that incorporates primitive “moral signaling” into a simple setting of indirect reciprocity. This model reveals some potential difficulties for the evolution of “moral signals.” We find that it is possible for “moral signals” to evolve alongside indirect reciprocity, but without some external pressure aiding the evolution of a signaling system, such a coevolution is unlikely.     

A tale of two defectors: the importance of standing for evolution of indirect reciprocity

Indirect reciprocity occurs when the cooperative behavior between two individuals is contingent on their previous behavior toward others. Previous theoretical analysis indicates that indirect reciprocity can evolve if individuals use an image-scoring strategy. In this paper, we show that, when errors are added, indirect reciprocity cannot be based on an image-scoring strategy. However, if individuals use a standing strategy, then cooperation through indirect reciprocity is evolutionarily stable. These two strategies differ with respect to the information to which they attend. While image-scoring strategies only need attend to the actions of others, standing strategies also require information about intent. We speculate that this difference may shed light on the evolvability of indirect reciprocity. Additionally, we show that systems of indirect reciprocity are highly sensitive to the availability of information. Finally, we present a model which shows that if indirect reciprocity were to evolve, selection should also favor trusting behavior in relations between strangers.     

Clustering in large networks does not promote upstream reciprocity

Upstream reciprocity (also called generalized reciprocity) is a putative mechanism for cooperation in social dilemma situations with which players help others when they are helped by somebody else. It is a type of indirect reciprocity. Although upstream reciprocity is often observed in experiments, most theories suggest that it is operative only when players form short cycles such as triangles, implying a small population size, or when it is combined with other mechanisms that promote cooperation on their own. An expectation is that real social networks, which are known to be full of triangles and other short cycles, may accommodate upstream reciprocity. In this study, I extend the upstream reciprocity game proposed for a directed cycle by Boyd and Richerson to the case of general networks. The model is not evolutionary and concerns the conditions under which the unanimity of cooperative players is a Nash equilibrium. I show that an abundance of triangles or other short cycles in a network does little to promote upstream reciprocity. Cooperation is less likely for a larger population size even if triangles are abundant in the network. In addition, in contrast to the results for evolutionary social dilemma games on networks, scale-free networks lead to less cooperation than networks with a homogeneous degree distribution.     

Cooperation can improve the resilience of common-pool resource systems against over-harvesting

Currently common-pool resource systems world-wide are under pressure due to overexploitation and environmental change. To ensure that these systems continue to provide vital ecosystem services it is necessary to sustain or increase their resilience against such pressure. One way of doing this may be to improve cooperation among agents who are heavily involved in common-pool resource systems, such as farmers, fishers, managers, and companies. Historical examples suggest that the persistence or collapse of common-pool resource systems may hinge on agents collaborating or not, but cooperation as a mechanism to improve resilience is not commonly included in existing models for studying resilience. Cooperation may be sustained through indirect reciprocity, i.e., cooperative behaviour by one agent that may be repaid by other agents. In this paper we develop a suite of agent-based models that represent an abstract version of a generic spatial common-pool resource system. This suite of models contains various mechanisms for cooperation based on trust. We investigate how the resilience of the models is affected by these mechanisms. The resilience of the models is assessed by applying various shocks which make it more difficult to gather resource, and measuring whether and how fast the agent population can recover from these shocks. The results suggest that although indirect reciprocity positively affects the level of cooperation in the system, cooperation could be common even without indirect reciprocity. It is shown that the presence of cooperation increases the resilience of the models against shocks.     

Generalized reciprocity in rats

The evolution of cooperation among nonrelatives has been explained by direct, indirect, and strong reciprocity. Animals should base the decision to help others on expected future help, which they may judge from past behavior of their partner. Although many examples of cooperative behavior exist in nature where reciprocity may be involved, experimental evidence for strategies predicted by direct reciprocity models remains controversial; and indirect and strong reciprocity have been found only in humans so far. Here we show experimentally that cooperative behavior of female rats is influenced by prior receipt of help, irrespective of the identity of the partner. Rats that were trained in an instrumental cooperative task (pulling a stick in order to produce food for a partner) pulled more often for an unknown partner after they were helped than if they had not received help before. This alternative mechanism, called generalized reciprocity, requires no specific knowledge about the partner and may promote the evolution of cooperation among unfamiliar nonrelatives.     

Multiple gossip statements and their effect on reputation and trustworthiness

Empirical and theoretical evidence from various disciplines indicates that reputation, reputation building and trust are important for human cooperation, social behaviour and economic progress. Recently, it has been shown that reputation gained in games of indirect reciprocity can be transmitted by gossip. But it has also been shown that gossiping has a strong manipulative potential. We propose that this manipulative potential is alleviated by the abundance of gossip. Multiple gossip statements give a better picture of the actual behaviour of a person, and thus inaccurate or fake gossip has little power as long as it is in the minority. In addition, we investigate the supposedly strong connection between reciprocity, reputation and trust. The results of this experimental study (with 11 groups of 12 students each) document that gossip quantity helps to direct cooperation towards cooperators. Moreover, reciprocity, trust and reputations transferred via gossip are positively correlated. This interrelation might have helped to reach the high levels of cooperation that can be observed in humans.     

Cooperation among non-relatives evolves by state-dependent generalized reciprocity

For decades, attempts to understand cooperation between non-kin have generated substantial theoretical and empirical interest in the evolutionary mechanisms of reciprocal altruism. There is growing evidence that the cognitive limitations of animals can hinder direct and indirect reciprocity because the necessary mental capacity is costly. Here, we show that cooperation can evolve by generalized reciprocity (help anyone, if helped by someone) even in large groups, if individuals base their decision to cooperate on a state variable updated by the outcome of the last interaction with an anonymous partner. We demonstrate that this alternative mechanism emerges through small evolutionary steps under a wide range of conditions. Since this state-based generalized reciprocity works without advanced cognitive abilities it may help to understand the evolution of complex social behaviour in a wide range of organisms.     

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

All social species face various “collective action problems” (CAPs) or “social dilemmas,” meaning problems in achieving cooperating when the best move from a selfish point of view yields an inferior collective outcome. Compared to most other species, humans are very good at solving these challenges, suggesting that something rather peculiar about human sociality facilitates collective action. This article proposes that language — the uniquely human faculty of symbolic communication — fundamentally alters the possibilities for collective action. I explore these issues using simple game-theoretic models and empirical evidence (both ethnographic and experimental). I review several standard mechanisms for the evolution of cooperation — mutualism, reciprocal altruism, indirect reciprocity and signaling — highlighting their limitations when it comes to explaining large-group cooperation, as well as the ways in which language helps overcome those limitations. Language facilitates complex coordination and is essential for establishing norms governing production efforts and distribution of collective goods that motivate people to cooperate voluntarily in large groups. Language also significantly lowers the cost of detecting and punishing “free riders,” thus greatly enhancing the scope and power of standard conditional reciprocity. In addition, symbolic communication encourages new forms of collectively beneficial displays and reputation management — what evolutionists often term “signaling” and “indirect reciprocity.” Thus, language reinforces existing forces that favor the evolution of cooperation, as well as creating new opportunities for collective action not available even to our closest primate relatives.     

The cost of cowardice: punitive sentiments towards free riders in Turkana raids

Models indicate that large-scale cooperation can be sustained by indirect reciprocity or direct punishment, but the relative importance of these mechanisms is unresolved. Unlike direct punishment, indirect sanctions can be meted out without cost to the sanctioner, but direct punishment is advantageous when the scale of cooperation exceeds the network size of individuals. It is of great interest to assess the importance of these mechanisms in small-scale acephalous groups in which people have lived for most of our evolutionary history. Here we evaluate sentiments towards free riders in combat among the Turkana, an acephalous nomadic pastoral society in East Africa who periodically mobilize for cattle-raids against neighboring ethnic groups. Using vignette studies, we probed participants’ motivation to sanction fictitious warriors who were cowards or deserters in a raid and compared it respectively to their reactions to an unskilled warrior or a warrior who turns back due to illness. Our results indicate that the Turkana are motivated to impose both indirect and direct sanctions on cowards consistent with indirect reciprocity and punishment models of cooperation. Our findings imply that both these mechanisms have shaped human cooperative psychology, and sheds light on how prestate societies solve the collective action problem in warfare.     

The influence of postreliance detection on the deceptive efficacy of dishonest signals of intent: Understanding facial clues to deceit as the outcome of signaling tradeoffs

Evolutionary communication theory posits that signalers and receivers are in a coevolutionary arms race. Receivers attempt to predict the behavior of signalers, and signalers attempt to manipulate the behavior of receivers (often through the use of dishonest signals of intent). This has led to the perception that deceitful signalers prefer perfectly deceptive signals. However, it is often easy for receivers to determine that a signal of intent was dishonest after relying on it to their detriment. Even the best deceivers may then acquire a reputation for being dishonest. For instance, in Prisoner's Dilemma (PD)-like social situations, predictable defectors make better social partners than unpredictable defectors. When opportunities to engage in social interaction depend on one's reputation for predictability, those who are better at concealing their defecting intentions may suffer the most from the reputations they acquire. Deceivers then face a tradeoff between the short-term benefits of successful deception and the long-term costs to their reputations. A mathematical model is developed and it is shown that the tradeoff often favors signalers who produce imperfectly deceptive signals over perfectly honest or perfectly deceptive ones. Implications for understanding human facial expressions and sociopathy are drawn.     

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

Evolution of cooperation among genetically unrelated individuals has been of considerable concern in various fields such as biology, economics, and psychology. The evolution of cooperation is often explained by reciprocity. Under reciprocity, cooperation can prevail in a society because a donor of cooperation receives reciprocation from the recipient of the cooperation, called direct reciprocity, or from someone else in the community, called indirect reciprocity. Nowak and Sigmund [1993. Chaos and the evolution of cooperation. Proc. Natl. Acad. Sci. USA 90, 5091-5094] have demonstrated that directly reciprocal cooperation in two-person prisoner's dilemma games with mutation of strategies can be maintained dynamically as periodic or chaotic oscillation. Furthermore, Eriksson and Lindgren [2005. Cooperation driven by mutations in multi-person Prisoner's Dilemma. J. Theor. Biol. 232, 399-409] have reported that directly reciprocal cooperation in n-person prisoner's dilemma games (n>2) can be maintained as periodic oscillation. Is dynamic cooperation observed only in direct reciprocity? Results of this study show that indirectly reciprocal cooperation in n-person prisoner's dilemma games can be maintained dynamically as periodic or chaotic oscillation. This is, to our knowledge, the first demonstration of chaos in indirect reciprocity. Furthermore, the results show that oscillatory dynamics are observed in common in the evolution of reciprocal cooperation whether for direct or indirect.     

A study of indirect reciprocity involving a reputation system or a simple tag system in a one-shot, multi-player game

The possibility of the evolution of cooperation backed by indirect reciprocity (IDR) in a one-shot, multi-player game is investigated focusing on two mechanisms. First of all, the reputation system with image score (RS with IS), as proposed by Nowak and Sigmund [Nowak, M.A., Sigmund, K., 1998. Evolution of indirect reciprocity by image scoring. Nature 393, 573–577], is investigated in various game structures. A numerical experiment demonstrates that the RS with IS is a robust mechanism for the support of IDR in various dilemma games, but whose effectiveness decreases with an increase in the number of players in a game. It is fair to say that the RS is an information mapping function to relate between player's cooperative fraction on his action and IS. As the second mechanism, a simple tag system which could be applicable to animals having no cognitive complexity is considered to support IDR. Computer simulations of the tag system's strategy for invading a population initially consisting of AllD, AllC, and Random strategies suggest several novel facts. The Tag strategy with plausible crossover and mutation probabilities can only invade to settle down if the game structure is not Trivial and contains a moderate dilemma. The Tag strategy's evolutionary competition takes place mainly in the presence of the AllD strategy. During the competition, the Tag strategy frequently metamorphoses to shake off the AllD strategy, but stops after winning in order to avoid a shrinking payoff due to fragmentation.     

Personal experience and reputation interact in human decisions to help reciprocally

There is ample evidence that human cooperative behaviour towards other individuals is often conditioned on information about previous interactions. This information derives both from personal experience (direct reciprocity) and from experience of others (i.e. reputation; indirect reciprocity). Direct and indirect reciprocity have been studied separately, but humans often have access to both types of information. Here, we experimentally investigate information use in a repeated helping game. When acting as donor, subjects can condition their decisions to help recipients with both types of information at a small cost to access such information. We find that information from direct interactions weighs more heavily in decisions to help, and participants tend to react less forgivingly to negative personal experience than to negative reputation. Moreover, effects of personal experience and reputation interact in decisions to help. If a recipient''s reputation is positive, the personal experience of the donor has a weak effect on the decision to help, and vice versa. Yet if the two types of information indicate conflicting signatures of helpfulness, most decisions to help follow personal experience. To understand the roles of direct and indirect reciprocity in human cooperation, they should be studied in concert, not in isolation.     

Reputation and the evolution of cooperation in sizable groups

The evolution of cooperation in social dilemmas has been of considerable concern in various fields such as sociobiology, economics and sociology. It might be that, in the real world, reputation plays an important role in the evolution of cooperation. Recently, studies that have addressed indirect reciprocity have revealed that cooperation can evolve through reputation, even though pairs of individuals interact only a few times. To our knowledge, most indirect reciprocity models have presumed dyadic interaction; no studies have attempted analysis of the evolution of cooperation in large communities where the effect of reputation is included. We investigate the evolution of cooperation in sizable groups in which the reputation of individuals affects the decision-making process. This paper presents the following: (i) cooperation can evolve in a four-person case, (ii) the evolution of cooperation becomes difficult as group size increases, even if the effect of reputation is included, and (iii) three kinds of final social states exist. In medium-sized communities, cooperative species can coexist in a stable manner with betrayal species.     

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

Indirect reciprocity is one of the major mechanisms of the evolution of cooperation. Because constant monitoring and accurate evaluation in moral assessments tend to be costly, indirect reciprocity can be exploited by cost evaders. A recent study crucially showed that a cooperative state achieved by indirect reciprocators is easily destabilized by cost evaders in the case with no supportive mechanism. Here, we present a simple and widely applicable solution that considers pre-assessment of cost evaders. In the pre-assessment, those who fail to pay for costly assessment systems are assigned a nasty image that leads to them being rejected by discriminators. We demonstrate that considering the pre-assessment can crucially stabilize reciprocal cooperation for a broad range of indirect reciprocity models. In particular for the most leading social norms, we analyse the conditions under which a prosocial state becomes locally stable.     

Dynamic indirect reciprocity; When is indirect reciprocity bounded by group membership?

Indirect reciprocity is a strong driver of reputation-based cooperation and previous studies have offered ample evidence as to when and how it guides cooperation towards others. However, the current empirical literature suffers from mixed evidence about the realm of indirect reciprocity; some studies showed that people assume that in-group members, but not out-group members belong to the same system of indirect reciprocity and they, thus, display reputation-based cooperation only towards in-group members. In other words, indirect reciprocity is bounded by group membership. On the other hand, other studies found that people display reputation-based cooperation towards out-group members as well, suggesting that indirect reciprocity is unbounded. Thus, there remains an important question to address. When is indirect reciprocity bounded by group membership? We carefully examined previous studies supporting bounded and unbounded indirect reciprocity perspectives and argue that the realm of indirect reciprocity is conditional to the presence of cues of reputational consequences (i.e., consequences of immediate cooperation). Based on our review, we further propose a new perspective, the dynamic indirect reciprocity perspective, which integrates bounded and unbounded indirect reciprocity perspectives. We propose a highly powered preregistered study to test hypotheses derived from the proposed perspective.     

Joint Effects of Asymmetric Payoff and Reciprocity Mechanisms on Collective Cooperation in Water Sharing Interactions: A Game Theoretic Perspective

Common-pool resource (CPR) dilemmas distinguish themselves from general public good problems by encompassing both social and physical features. This paper examines how a physical mechanism, namely asymmetric payoff; and a social mechanism, reciprocity; simultaneously affect collective cooperation in theoretical water sharing interactions. We present an iterative N-person game theoretic model to investigate the joint effects of these two mechanisms in a linear fully connected river system under three information assumptions. From a simple evolutionary perspective, this paper quantitatively addresses the conditions for Nash Equilibrium in which collective cooperation might be established. The results suggest that direct reciprocity increases every actor’s motivation to contribute to the collective good of the river system. Meanwhile, various upstream and downstream actors manifest individual disparities as a result of the direct reciprocity and asymmetric payoff mechanisms. More specifically, the downstream actors are less willing to cooperate unless there is a high probability that long-term interactions are ensured; however, a greater level of asymmetries is likely to increase upstream actors’ incentives to cooperate even though the interactions could quickly end. The upstream actors also display weak sensitivity to an increase in the total number of actors, which generally results in a reduction in the other actors’ motivation for cooperation. It is also shown that the indirect reciprocity mechanism relaxes the overall conditions for cooperative Nash Equilibrium.     

Contingent movement and cooperation evolve under generalized reciprocity

How cooperation and altruism among non-relatives can persist in the face of cheating remains a key puzzle in evolutionary biology. Although mechanisms such as direct and indirect reciprocity and limited movement have been put forward to explain such cooperation, they cannot explain cooperation among unfamiliar, highly mobile individuals. Here we show that cooperation may be evolutionarily stable if decisions taken to cooperate and to change group membership are both dependent on anonymous social experience (generalized reciprocity). We find that a win-stay, lose-shift rule (where shifting is either moving away from the group or changing tactics within the group after receiving defection) evolves in evolutionary simulations when group leaving is moderately costly (i.e. the current payoff to being alone is low, but still higher than that in a mutually defecting group, and new groups are rarely encountered). This leads to the establishment of widespread cooperation in the population. If the costs of group leaving are reduced, a similar group-leaving rule evolves in association with cooperation in pairs and exploitation of larger anonymous groups. We emphasize that mechanisms of assortment within populations are often behavioural decisions and should not be considered independently of the evolution of cooperation.     

The long-term benefits of human generosity in indirect reciprocity

Among the theories that have been proposed to explain the evolution of altruism are direct reciprocity and indirect reciprocity. The idea of the latter is that helping someone or refusing to do so has an impact on one's reputation within a group. This reputation is constantly assessed and reassessed by others and is taken into account by them in future social interactions. Generosity in indirect reciprocity can evolve if and only if it eventually leads to a net benefit in the long term. Here, we show that this key assumption is met. We let 114 students play for money in an indirect and a subsequent direct reciprocity game. We found that although being generous, i.e., giving something of value to others, had the obvious short-term costs, it paid in the long run because it builds up a reputation that is rewarded by third parties (who thereby themselves increase their reputation). A reputation of being generous also provided an advantage in the subsequent direct reciprocity game, probably because it builds up trust that can lead to more stable cooperation.