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.     

How is the equilibrium of continuous strategy game different from that of discrete strategy game?

Cooperation in the prisoner's dilemma (PD) played on various networks has been explained by so-called network reciprocity. Most of the previous studies presumed that players can offer either cooperation (C) or defection (D). This discrete strategy seems unrealistic in the real world, since actual provisions might not be discrete, but rather continuous. This paper studies the differences between continuous and discrete strategies in two aspects under the condition that the payoff function of the former is a linear interpolation of the payoff matrix of the latter. The first part of this paper proves theoretically that for two-player games, continuous and discrete strategies have different equilibria and game dynamics in a well-mixed but finite population. The second part, conducting a series of numerical experiments, reveals that such differences become considerably large in the case of PD games on networks. Furthermore, it shows, using the Wilcoxon sign-rank test, that continuous and discrete strategy games are statistically significantly different in terms of equilibria. Intensive discussion by comparing these two kinds of games elucidates that describing a strategy as a real number blunts D strategy invasion to C clusters on a network in the early stage of evolution. Thus, network reciprocity is enhanced by the continuous strategy.     

THE ENFORCEMENT OF COOPERATION BY POLICING

Policing is regarded as an important mechanism for maintaining cooperation in human and animal social groups. A simple model providing a theoretical overview of the coevolution of policing and cooperation has been analyzed by Frank (1995, 1996b, 2003, 2009) , and this suggests that policing will evolve to fully suppress cheating within social groups when relatedness is low. Here, we relax some of the assumptions made by Frank, and investigate the consequences for policing and cooperation. First, we address the implicit assumption that the individual cost of investment into policing is reduced when selfishness dominates. We find that relaxing this assumption leads to policing being favored only at intermediate relatedness. Second, we address the assumption that policing fully recovers the loss of fitness incurred by the group owing to selfishness. We find that relaxing this assumption prohibits the evolution of full policing. Finally, we consider the impact of demography on the coevolution of policing and cooperation, in particular the role for kin competition to disfavor the evolution of policing, using both a heuristic “open” model and a “closed” island model. We find that large groups and increased kin competition disfavor policing, and that policing is maintained more readily than it invades. Policing may be harder to evolve than previously thought.     

Evolutionary dynamics of continuous strategy games on graphs and social networks under weak selection

Understanding the emergence of cooperation among selfish individuals has been a long-standing puzzle, which has been studied by a variety of game models. Most previous studies presumed that interactions between individuals are discrete, but it seems unrealistic in real systems. Recently, there are increasing interests in studying game models with a continuous strategy space. Existing research work on continuous strategy games mainly focuses on well-mixed populations. Especially, little theoretical work has been conducted on their evolutionary dynamics in a structured population. In the previous work (Zhong et al., BioSystems, 2012), we showed that under strong selection, continuous and discrete strategies have significantly different equilibrium and game dynamics in spatially structured populations. In this paper, we further study evolutionary dynamics of continuous strategy games under weak selection in structured populations. By using the fixation probability based stochastic dynamics, we derive exact conditions of natural selection favoring cooperation for the death–birth updating scheme. We also present a network gain decomposition of the game equilibrium, which might provide a new view of the network reciprocity in a quantitative way. Finally, we make a detailed comparison between games using discrete and continuous strategies. As compared to the former, we find that for the latter (i) the same selection conditions are derived for the general 2 × 2 game; especially, the rule b/c > k in a simplified Prisoner's Dilemma is valid as well; however, (ii) for a coordination game, interestingly, the risk-dominant strategy is disfavored. Numerical simulations have also been conducted to validate our results.     

ASSORTMENT AND THE EVOLUTION OF GENERALIZED RECIPROCITY

Reciprocity is often invoked to explain cooperation. Reciprocity is cognitively demanding, and both direct and indirect reciprocity require that individuals store information about the propensity of their partners to cooperate. By contrast, generalized reciprocity, wherein individuals help on the condition that they received help previously, only relies on whether an individual received help in a previous encounter. Such anonymous information makes generalized reciprocity hard to evolve in a well‐mixed population, as the strategy will lose out to pure defectors. Here we analyze a model for the evolution of generalized reciprocity, incorporating assortment of encounters, to investigate the conditions under which it will evolve. We show that, in a well‐mixed population, generalized reciprocity cannot evolve. However, incorporating assortment of encounters can favor the evolution of generalized reciprocity in which indiscriminate cooperation and defection are both unstable. We show that generalized reciprocity can evolve under both the prisoner's dilemma and the snowdrift game.     

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.     

Hunter–Gatherer population structure and the evolution of contingent cooperation

Unlike other vertebrates, humans cooperate in large groups with unrelated individuals. Many authors have argued that the evolution of such cooperation has resulted from reciprocity and other forms of contingent cooperation. This argument is not well supported by existing theory. The theory of contingent cooperation in pairs is well developed: reciprocating strategies are stable when common, and can increase when rare as long as population structure leads to modest levels of relatedness. In larger groups, however, it is not clear whether contingent cooperation can increase when rare. Existing work suggests that contingent strategies cannot increase unless relatedness is high, but depends on unrealistic assumptions about the effects of population structure. Here we develop and analyze a model incorporating a two level population structure that captures important features of human hunter–gatherer societies. This model suggests that previous work underestimates the range of conditions under which contingent cooperation can evolve, but also predicts that cooperation will not evolve unless (1) social groups are small, and (2) the relatedness within ethnolinguistic groups is at the high end of the range of empirical estimates.     

Evolution of cooperation through indirect reciprocity

How can cooperation through indirect reciprocity evolve and what would it be like? This problem has previously been studied by simulating evolution in a small group of interacting individuals, assuming no gene flow between groups. In these simulations, certain ''image scoring'' strategies were found to be the most successful. However, analytical arguments show that it would not be in an individual''s interest to use these strategies. Starting with this puzzle, we investigate indirect reciprocity in simulations based on an island model. This has an advantage in that the role of genetic drift can be examined. Our results show that the image scoring strategies depend on very strong drift or a very small cost of giving help. As soon as these factors are absent, selection eliminates image scoring. We also consider other possibilities for the evolution of indirect reciprocity. In particular, we find that the strategy of aiming for ''good standing'' has superior properties. It can be an evolutionarily stable strategy and, even if not, it usually beats image scoring. Furthermore, by introducing quality variation among individuals into the model, we show that the standing strategy can be quality revealing, adding a new dimension to indirect reciprocity. Finally, we discuss general problems with currently popular modelling styles.     

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.     

Dynamic-persistence of cooperation in public good games when group size is dynamic

The evolution of cooperation is possible with a simple model of a population of agents that can move between groups. The agents play public good games within their group. The relative fitness of individuals within the whole population affects their number of offspring. Groups of cooperators evolve but over time are invaded by defectors which eventually results in the group's extinction. However, for small levels of migration and mutation, high levels of cooperation evolve at the population level. Thus, evolution of cooperation based on individual fitness without kin selection, indirect or direct reciprocity is possible. We provide an analysis of the parameters that affect cooperation, and describe the dynamics and distribution of population sizes over time.     

Direct Reciprocity in Spatial Populations Enhances R-Reciprocity As Well As ST-Reciprocity

As is well-known, spatial reciprocity plays an important role in facilitating the emergence of cooperative traits, and the effect of direct reciprocity is also obvious for explaining the cooperation dynamics. However, how the combination of these two scenarios influences cooperation is still unclear. In the present work, we study the evolution of cooperation in 2×2 games via considering both spatial structured populations and direct reciprocity driven by the strategy with 1-memory length. Our results show that cooperation can be significantly facilitated on the whole parameter plane. For prisoner''s dilemma game, cooperation dominates the system even at strong dilemma, where maximal social payoff is still realized. In this sense, R-reciprocity forms and it is robust to the extremely strong dilemma. Interestingly, when turning to chicken game, we find that ST-reciprocity is also guaranteed, through which social average payoff and cooperation is greatly enhanced. This reciprocity mechanism is supported by mean-field analysis and different interaction topologies. Thus, our study indicates that direct reciprocity in structured populations can be regarded as a more powerful factor for the sustainability of cooperation.     

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.     

THE EVOLUTIONARILY STABLE PHENOTYPE DISTRIBUTION IN A RANDOM ENVIRONMENT

In an unpredictably changing environment, phenotypic variability may evolve as a “bet-hedging” strategy. We examine here two models for evolutionarily stable phenotype distributions resulting from stabilizing selection with a randomly fluctuating optimum. Both models include overlapping generations, either survival of adults or a dormant propagule pool. In the first model (mixed-strategies model) we assume that individuals can produce offspring with a distribution of phenotypes, in which case, the evolutionarily stable population always consists of a single genotype. We show that there is a unique evolutionarily stable strategy (ESS) distribution that does not depend on the amount of generational overlap, and that the ESS distribution generically is discrete rather than continuous; that is, there are distinct classes of offspring rather than a continuous distribution of offspring phenotypes. If the probability of extreme fluctuations in the optimum is sufficiently small, then the ESS distribution is monomorphic: a single type fitted to the mean environment. At higher levels of variability, the ESS distribution is polymorphic, and we find stability conditions for dimorphic distributions. For an exponential or similarly broad-tailed distribution of the optimum phenotype, the ESS consists of an infinite number of distinct phenotypes. In the second model we assume that an individual produces offspring with a single, genetically determined phenotype (pure-strategies model). The ESS population then contains multiple genotypes when the environmental variance is sufficiently high. However the phenotype distributions are similar to those in the mixed-strategies model: discrete, with an increasing number of distinct phenotypes as the environmental variance increases.     

A friend in need is a friend indeed: Need-based sharing,rather than cooperative assortment,predicts experimental resource transfers among Agta hunter-gatherers

Despite much theorizing, the evolutionary reasons why humans cooperate extensively with unrelated individuals are still largely unknown. While reciprocity explains many instances of non-kin cooperation, much remains to be understood. A recent suite of models based upon ‘cooperative assortativity’ suggest that non-kin cooperation can evolve if individuals preferentially assort with certain cooperative phenotypes, such as helping those who help others. Here, we test these assortative hypotheses among the Agta, a population of Filipino hunter-gatherers, using an experimental resource allocation game in which individuals divide resources between themselves and camp-mates. Individuals preferentially shared with less cooperative individuals, arguing against cooperative assortativity as a mechanism sustaining resource transfers in this population. Rather, sharing was often based on the recipient's level of need, in addition to kin-based transfers and reciprocal sharing. Contrary to several recent theoretical accounts, in this real-world setting we find no evidence for cooperative assortativity influencing patterns of cooperation. These results may reflect the demands of living in a foraging ecology characterized by high resource stochasticity, necessitating need-based sharing as a system of long-term reciprocity to mitigate repeated subsistence shortfalls.     

Correlated pay-offs are key to cooperation

The general belief that cooperation and altruism in social groups result primarily from kin selection has recently been challenged, not least because results from cooperatively breeding insects and vertebrates have shown that groups may be composed mainly of non-relatives. This allows testing predictions of reciprocity theory without the confounding effect of relatedness. Here, we review complementary and alternative evolutionary mechanisms to kin selection theory and provide empirical examples of cooperative behaviour among unrelated individuals in a wide range of taxa. In particular, we focus on the different forms of reciprocity and on their underlying decision rules, asking about evolutionary stability, the conditions selecting for reciprocity and the factors constraining reciprocal cooperation. We find that neither the cognitive requirements of reciprocal cooperation nor the often sequential nature of interactions are insuperable stumbling blocks for the evolution of reciprocity. We argue that simple decision rules such as ‘help anyone if helped by someone’ should get more attention in future research, because empirical studies show that animals apply such rules, and theoretical models find that they can create stable levels of cooperation under a wide range of conditions. Owing to its simplicity, behaviour based on such a heuristic may in fact be ubiquitous. Finally, we argue that the evolution of exchange and trading of service and commodities among social partners needs greater scientific focus.     

Evolution of spite through indirect reciprocity

How can cooperation persist in the face of a temptation to ''cheat''? Several recent papers have suggested that the answer may lie in indirect reciprocity. Altruistic individuals may benefit by eliciting altruism from observers, rather than (as in direct reciprocity) from the recipient of the aid they provide. Here, we point out that indirect reciprocity need not always favour cooperation; by contrast, it may support spiteful behaviour, which is costly for the both actor and recipient. Existing theory suggests spite is unlikely to persist, but we demonstrate that it may do so when spiteful individuals are less likely to incur aggression from observers (a negative form of indirect reciprocity).     

Upstream reciprocity and the evolution of gratitude

If someone is nice to you, you feel good and may be inclined to be nice to somebody else. This every day experience is borne out by experimental games: the recipients of an act of kindness are more likely to help in turn, even if the person who benefits from their generosity is somebody else. This behaviour, which has been called ‘upstream reciprocity’, appears to be a misdirected act of gratitude: you help somebody because somebody else has helped you. Does this make any sense from an evolutionary or a game theoretic perspective? In this paper, we show that upstream reciprocity alone does not lead to the evolution of cooperation, but it can evolve and increase the level of cooperation if it is linked to either direct or spatial reciprocity. We calculate the random walks of altruistic acts that are induced by upstream reciprocity. Our analysis shows that gratitude and other positive emotions, which increase the willingness to help others, can evolve in the competitive world of natural selection.     

Network homophily and the evolution of the pay-it-forward reciprocity

The pay-it-forward reciprocity is a type of cooperative behavior that people who have benefited from others return favors to third parties other than the benefactors, thus pushing forward a cascade of kindness. The phenomenon of the pay-it-forward reciprocity is ubiquitous, yet how it evolves to be part of human sociality has not been fully understood. We develop an evolutionary dynamics model to investigate how network homophily influences the evolution of the pay-it-forward reciprocity. Manipulating the extent to which actors carrying the same behavioral trait are linked in networks, the computer simulation model shows that strong network homophily helps consolidate the adaptive advantage of cooperation, yet introducing some heterophily to the formation of network helps advance cooperation's scale further. Our model enriches the literature of inclusive fitness theory by demonstrating the conditions under which cooperation or reciprocity can be selected for in evolution when social interaction is not confined exclusively to relatives.     

Direct reciprocity with costly punishment: generous tit-for-tat prevails

The standard model for direct reciprocity is the repeated Prisoner's Dilemma, where in each round players choose between cooperation and defection. Here we extend the standard framework to include costly punishment. Now players have a choice between cooperation, defection and costly punishment. We study the set of all reactive strategies, where the behavior depends on what the other player has done in the previous round. We find all cooperative strategies that are Nash equilibria. If the cost of cooperation is greater than the cost of punishment, then the only cooperative Nash equilibrium is generous-tit-for-tat (GTFT), which does not use costly punishment. If the cost of cooperation is less than the cost of punishment, then there are infinitely many cooperative Nash equilibria and the response to defection can include costly punishment. We also perform computer simulations of evolutionary dynamics in populations of finite size. These simulations show that in the context of direct reciprocity, (i) natural selection prefers generous tit-for-tat over strategies that use costly punishment, and (ii) that costly punishment does not promote the evolution of cooperation. We find quantitative agreement between our simulation results and data from experimental observations.     

Mechanistic constraints and the unlikely evolution of reciprocal cooperation

Social evolution theory faces a puzzle: a gap between theoretical and empirical results on reciprocity. On the one hand, models show that reciprocity should evolve easily in a wide range of circumstances. On the other hand, empirically, few clear instances of reciprocity (even in a broad sense) have been found in nonhuman animals. In this paper, I aim to suggest and evaluate a novel reason concurring to solve this puzzle. I propose that it is difficult for reciprocity to evolve because it raises an evolutionary problem of bootstrapping: it requires that two complementary functions: (i) the ability to cooperate and (ii) the ability to respond conditionally to the cooperation of others, arise together and reach a significant frequency, whereas neither of them can be favoured in the absence of the other. I develop analytical models and simulations showing that, for this reason, the evolutionary emergence of reciprocal cooperation is highly unlikely. I then discuss the consequences of this result for our understanding of cooperation.