Indirect reciprocity among imperfect individuals

Reciprocal cooperation occurs when the overall benefits of receiving help exceed the costs of donating help (Q. Rev. Biol. 46 (197) 35). That is, individuals in good condition--for whom the pertinent costs are relatively small; donate help in order to secure reciprocity in their hour of need--when the benefits of receiving a donation are large. Consequently, reciprocity occurs among individuals who occasionally need help. In particular, such individuals will be unable to help others, no matter how deserving, when in need of help themselves--involuntary defection. This paper deals with the effects of involuntary defection in the context of a specific model of indirect reciprocity (i.e. reciprocal altruism that is directed toward all the cooperative members of the community) due to Nowak and Sigmund (J. Theor. Biol.194 (1998b) 561: Sections 2-4). In that model, the authors formulate the decision rules for conditional cooperation in the context of indirect reciprocity, and demonstrate that these decision rules can account for a long-term persistence of cooperation. Here we show that addition of involuntary defection to the decision rules formulated by Nowak and Sigmund results in indirect reciprocity that is evolutionary stable under appropriate conditions. Moreover, for a wide range of parameter values, evolutionary stability of cooperation requires a mixture of conditional- and unconditional-altruist behaviors. To recollect, unconditional altruist strategy can be viewed as conditional altruist strategy sans the ability to decide when the help-soliciting individual should be refused help. That is, given involuntary defection, stability of cooperation requires an occasional forgiveness, if only by default, of a failure to donate help. Thus, we see that evolutionary stable indirect reciprocity does not require perfection in either the ability to assess the merits of the help-soliciting individuals, or the ability to donate help when it is merited. On the contrary, we are forced to conclude that reciprocity, at least in the current case, is stable only among imperfect individuals.     

Tag-based indirect reciprocity by incomplete social information

Evolution of altruistic behaviour in interacting individuals is accounted for by, for example, kin selection, direct reciprocity, spatially limited interaction and indirect reciprocity. Real social agents, particularly humans, often take actions based on similarity between themselves and others. Although tag-based indirect reciprocity in which altruism occurs exclusively among similar flocks is a natural expectation, its mechanism has not really been established. We propose a model of tag-based indirect reciprocity by assuming that each player may note strategies of others. We show that tag-based altruism can evolve to eradicate other strategies, including unconditional defectors for various initial strategy configurations and parameter sets. A prerequisite for altruism is that the strategy is sometimes, but not always, visible to others. Without visibility of strategies, policing does not take place and defection is optimal. With perfect visibility, what a player does is always witnessed by others and cooperation is optimal. In the intermediate regime, discriminators based on tag proximity, rather than mixture of generous players and defectors, are most likely to evolve. In this situation, altruism is realized based on homophily in which players are exclusively good to similar others.     

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.     

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.     

A conditional Markov model for clustered progressive multistate processes under incomplete observation

Clustered progressive chronic disease processes arise when interest lies in modeling damage in paired organ systems (e.g., kidneys, eyes), in diseases manifest in different organ systems, or in systemic conditions for which damage may occur in several locations of the body. Multistate Markov models have considerable appeal for modeling damage in such settings, particularly when patients are only under intermittent observation. Generalizations are necessary, however, to deal with the fact that processes within subjects may not be independent. We describe a conditional Markov model in which the clustering in processes within subjects is addressed by the use of multiplicative random effects for each transition intensity. The random effects for the different transition intensities may be correlated within subjects, but are assumed to be independent for different subjects. We apply the mixed Markov model to a motivating data set of patients with psoriatic arthritis, and characterize the progressive course of damage in joints of the hand. A generalization to accommodate a subpopulation of "stayers" and extensions which facilitate regression are indicated and illustrated.     

Indirect reciprocity in asymmetric interactions: when apparent altruism facilitates profitable exploitation

Intraspecific cooperation and interspecific mutualism often feature an asymmetry in the scope for exploitation. We investigate the evolution of indirect reciprocity in an asymmetric game, loosely modelled on interactions between cleaner fishes and clients, in which 'actors' can choose to help or to exploit a 'recipient' that approaches them, while recipients can only choose whether or not to approach an actor (based on the observation of its behaviour towards others). We show that when actors vary in state over time, in a manner that influences the potential gains from exploitation, an equilibrium is possible at which recipients avoid actors whom they have observed exploiting others in the past, and actors help when the potential gains from exploitation are low but choose to exploit when the potential gains are high. In this context, helping is favoured not because it elicits reciprocal altruism ('help so that you may be helped'), but because it facilitates profitable exploitation ('help so that you may gain the opportunity to harm'). The cost of helping one recipient is thereby recouped through exploitation of another. Indirect reciprocity is thus possible even in asymmetric interactions in which one party cannot directly 'punish' exploitation or 'reward' helping by the other.     

Indirect reciprocity and tradeoff paradigms in the wake of violent intergroup conflict

Intergroup interaction can be hindered by legacies of conflict and group biases. Many studies have looked at intergroup attitudes and pro-sociality in the wake of intergroup conflict, but few have explicitly studied how the group affiliation of another person affects the willingness to interact economically, especially when the interactions concern contested issues. In this study, I investigate the effect of group affiliation on the willingness to engage in economic interactions with others among individuals exposed to violent intergroup conflict, using a sample of refugees from the conflicts in Syria and Iraq. Based on the theory of indirect reciprocity, it is predicted that the tradeoff paradigms, that is, the willingness to engage in economic transactions with another individual, will depend on previous actions of other members of that individual's group. Participants tended to adopt a communal sharing tradeoff paradigm with ingroup members, and they tended to adopt a market pricing paradigm with outgroup members. However, this was the case only for those who reported that outgroup members had taken actions to harm them or their family in the conflict. For those who reported being harmed by members of the ingroup, a market pricing paradigm was employed also with ingroup members. The results suggest that group biases and indirect reciprocity after violent conflict do not necessarily arise from group identities alone, but as a function of past interactions with outgroup members.     

Cooperation under indirect reciprocity and imitative trust

Indirect reciprocity, a key concept in behavioral experiments and evolutionary game theory, provides a mechanism that allows reciprocal altruism to emerge in a population of self-regarding individuals even when repeated interactions between pairs of actors are unlikely. Recent empirical evidence show that humans typically follow complex assessment strategies involving both reciprocity and social imitation when making cooperative decisions. However, currently, we have no systematic understanding of how imitation, a mechanism that may also generate negative effects via a process of cumulative advantage, affects cooperation when repeated interactions are unlikely or information about a recipient's reputation is unavailable. Here we extend existing evolutionary models, which use an image score for reputation to track how individuals cooperate by contributing resources, by introducing a new imitative-trust score, which tracks whether actors have been the recipients of cooperation in the past. We show that imitative trust can co-exist with indirect reciprocity mechanisms up to a threshold and then cooperation reverses -revealing the elusive nature of cooperation. Moreover, we find that when information about a recipient's reputation is limited, trusting the action of third parties towards her (i.e. imitating) does favor a higher collective cooperation compared to random-trusting and share-alike mechanisms. We believe these results shed new light on the factors favoring social imitation as an adaptive mechanism in populations of cooperating social actors.     

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.     

Three-person game facilitates indirect reciprocity under image scoring

Reputation building plays an important role in the evolution of reciprocal altruism when the same individuals do not interact repeatedly because, by referring to reputation, a reciprocator can know which partners are cooperative and can reciprocate with a cooperator. This reciprocity based on reputation is called indirect reciprocity. Previous studies of indirect reciprocity have focused only on two-person games in which only two individuals participate in a single interaction, and have claimed that indirectly reciprocal cooperation cannot be established under image scoring reputation criterion where the reputation of an individual who has cooperated (defected) becomes good (bad). In this study, we specifically examine three-person games, and reveal that indirectly reciprocal cooperation can be formed and maintained stably, even under image scoring, by a nucleus shield mechanism. In the nucleus shield, reciprocators are a shield that keeps out unconditional defectors, whereas unconditional cooperators are the backbone of cooperation that retains a good reputation among the population.     

Repeated games and direct reciprocity under active linking

Direct reciprocity relies on repeated encounters between the same two individuals. Here we examine the evolution of cooperation under direct reciprocity in dynamically structured populations. Individuals occupy the vertices of a graph, undergoing repeated interactions with their partners via the edges of the graph. Unlike the traditional approach to evolutionary game theory, where individuals meet at random and have no control over the frequency or duration of interactions, we consider a model in which individuals differ in the rate at which they seek new interactions. Moreover, once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. Whenever the active dynamics of links is sufficiently fast, population structure leads to a simple transformation of the payoff matrix, effectively changing the game under consideration, and hence paving the way for reciprocators to dominate defectors. We derive analytical conditions for evolutionary stability.     

One-shot reciprocity under error management is unbiased and fragile

The error management model of altruism in one-shot interactions provides an influential explanation for one of the most controversial behaviors in evolutionary social science. The model posits that one-shot altruism arises from a domain-specific cognitive bias that avoids the error of mistaking a long-term relationship for a one-shot interaction. One-shot altruism is thus, in an intriguingly paradoxical way, a form of reciprocity. We examine the logic behind this idea in detail. In its most general form the error management model is exceedingly flexible, and restrictions about the psychology of agents are necessary for selection to be well-defined. Once these restrictions are in place, selection is well defined, but it leads to behavior that is perfectly consistent with an unbiased rational benchmark. Thus, the evolution of one-shot reciprocity does not require an evoked cognitive bias based on repeated interactions and reputation. Moreover, in spite of its flexibility in terms of psychology, the error management model assumes that behavior is exceedingly rigid when individuals face a new interaction partner. Reciprocity can only take the form of tit-for-tat, and individuals cannot adjust their behavior in response to new information about the duration of a relationship. Zefferman (2014) showed that one-shot reciprocity does not reliably evolve if one relaxes the first restriction, and we show that the behavior does not reliably evolve if one relaxes the second restriction. Altogether, these theoretical results on one-shot reciprocity do not square well with experiments showing increased altruism in the presence of payoff-irrelevant stimuli that suggest others are watching.     

First observation of incomplete vertical circulation in Lake Biwa

Limnology - Vertical circulation reaches the bottom of the deepest (> 90 m) part of the northern basin of Lake Biwa, a warm monomictic lake, during winter (January to March)...     

On intrapersonal reciprocity

The existence of conflicts between different sets of genes within the genome is now widely accepted. But where there is conflict, there are also benefits to be gained from cooperation between the contending parties to reduce conflict costs. The potential for reciprocal altruism [Trivers, 1971] within an individual organism has hitherto attracted little attention but raises the possibility of complex interactions within the self.     

Testing the Mendelian segregation ratio under incomplete ascertainment.

The properties of a test, suggested by HALDANE [1938], for a Mendelian segregation ratio of 0.25 when ascertainment is incomplete are investigated. The error rates associated with this procedure show the weakness of this specific test. An alternative test based on a chi2 statistic is illustrated with the data on human albinism originally analyzed by HALDANE [1938].     

Stern-judging: A simple, successful norm which promotes cooperation under indirect reciprocity

We study the evolution of cooperation under indirect reciprocity, believed to constitute the biological basis of morality. We employ an evolutionary game theoretical model of multilevel selection, and show that natural selection and mutation lead to the emergence of a robust and simple social norm, which we call stern-judging. Under stern-judging, helping a good individual or refusing help to a bad individual leads to a good reputation, whereas refusing help to a good individual or helping a bad one leads to a bad reputation. Similarly for tit-for-tat and win-stay-lose-shift, the simplest ubiquitous strategies in direct reciprocity, the lack of ambiguity of stern-judging, where implacable punishment is compensated by prompt forgiving, supports the idea that simplicity is often associated with evolutionary success.