Collective Chasing Behavior between Cooperators and Defectors in the Spatial Prisoner’s Dilemma

Cooperation is one of the essential factors for all biological organisms in major evolutionary transitions. Recent studies have investigated the effect of migration for the evolution of cooperation. However, little is known about whether and how an individuals’ cooperativeness coevolves with mobility. One possibility is that mobility enhances cooperation by enabling cooperators to escape from defectors and form clusters; the other possibility is that mobility inhibits cooperation by helping the defectors to catch and exploit the groups of cooperators. In this study we investigate the coevolutionary dynamics by using the prisoner’s dilemma game model on a lattice structure. The computer simulations demonstrate that natural selection maintains cooperation in the form of evolutionary chasing between the cooperators and defectors. First, cooperative groups grow and collectively move in the same direction. Then, mutant defectors emerge and invade the cooperative groups, after which the defectors exploit the cooperators. Then other cooperative groups emerge due to mutation and the cycle is repeated. Here, it is worth noting that, as a result of natural selection, the mobility evolves towards directional migration, but not to random or completely fixed migration. Furthermore, with directional migration, the rate of global population extinction is lower when compared with other cases without the evolution of mobility (i.e., when mobility is preset to random or fixed). These findings illustrate the coevolutionary dynamics of cooperation and mobility through the directional chasing between cooperators and defectors.     

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.     

The leading eight: social norms that can maintain cooperation by indirect reciprocity

The theory of indirect reciprocation explains the evolution of cooperation among unrelated individuals, engaging in one-shot interaction. Using reputation, a player acquires information on who are worth cooperating and who are not. In a previous paper, we formalized the reputation dynamics, a rule to assign a binary reputation (good or bad) to each player when his action, his current reputation, and the opponent's reputation are given. We then examined all the possible reputation dynamics, and found that there exist only eight reputation dynamics named "leading eight" that can maintain the ESS with a high level of cooperation, even if errors are included in executing intended cooperation and in reporting the observation to the public. In this paper, we study the nature of these successful social norms. First, we characterize the role of each pivot of the reputation dynamics common to all of the leading eight. We conclude that keys to the success in indirect reciprocity are to be nice (maintenance of cooperation among themselves), retaliatory (detection of defectors, punishment, and justification of punishment), apologetic, and forgiving. Second, we prove the two basic properties of the leading eight, which give a quantitative evaluation of the ESS condition and the level of cooperation maintained at the ESS.     

Multiple reputation domains and cooperative behaviour in two Latin American communities

Reputations are a ubiquitous feature of human social life, and a large literature has been dedicated to explaining the relationship between prosocial reputations and cooperation in social dilemmas. However, humans form reputations in domains other than prosociality, such as economic competency that could affect cooperation. To date, no research has evaluated the relative effects of multiple reputation domains on cooperation. To bridge this gap, we analyse how prosocial and competency reputations affect cooperation in two Latin American communities (Bwa Mawego, Dominica, and Pucucanchita, Peru) across a number of social contexts (Dominica: labour contracting, labour exchange and conjugal partnership formation; Peru: agricultural and health advice network size). First, we examine the behavioural correlates of prosocial and competency reputations. Following, we analyse whether prosocial, competency, or both reputation domains explain the flow of cooperative benefits within the two communities. Our analyses suggest that (i) although some behaviours affect both reputation domains simultaneously, each reputation domain has a unique behavioural signature; and (ii) competency reputations affect cooperation across a greater number of social contexts compared to prosocial reputations. Results are contextualized with reference to the social markets in which behaviour is embedded and a call for greater theory development is stressed.     

Partner Choice Drives the Evolution of Cooperation via Indirect Reciprocity

Indirect reciprocity potentially provides an important means for generating cooperation based on helping those who help others. However, the use of ‘image scores’ to summarize individuals’ past behaviour presents a dilemma: individuals withholding help from those of low image score harm their own reputation, yet giving to defectors erodes cooperation. Explaining how indirect reciprocity could evolve has therefore remained problematic. In all previous treatments of indirect reciprocity, individuals are assigned potential recipients and decide whether to cooperate or defect based on their reputation. A second way of achieving discrimination is through partner choice, which should enable individuals to avoid defectors. Here, I develop a model in which individuals choose to donate to anyone within their group, or to none. Whereas image scoring with random pairing produces cycles of cooperation and defection, with partner choice there is almost maximal cooperation. In contrast to image scoring with random pairing, partner choice results in almost perfect contingency, producing the correlation between giving and receiving required for cooperation. In this way, partner choice facilitates much higher and more stable levels of cooperation through image scoring than previously reported and provides a simple mechanism through which systems of helping those who help others can work.     

Reputation-based conditional interaction supports cooperation in well-mixed prisoner's dilemmas

In the well-mixed prisoner's dilemma game, individuals are typically assumed to have no choice about whether to interact with other individuals in the population. In this paper, we instead consider reputation-based conditional interaction and its consequences for the evolution of cooperation. Each individual has a tolerance range, and only interacts with other individuals whose reputation lies within its tolerance range in a chosen sample of the population. Reputation contains information about the number of interaction partners an individual has just cooperated with. We find that the introduction of conditional interaction promotes cooperation in well-mixed populations, and there exist moderate tolerance ranges for which this effect is maximized. For a given tolerance range, there is a critical cost-to-benefit ratio below which cooperation can be promoted. Interestingly, we find that if cooperation evolves, different cooperators' interaction clusters are typically maintained in the population, each around a different reputation level. We further investigate some properties of these cooperators' clusters. Moreover, we examine the effects of the sample number on the evolution of cooperation. Our results highlight the importance of the detailed consideration of modes of interaction for the evolution of cooperation in well-mixed populations.     

Global analyses of evolutionary dynamics and exhaustive search for social norms that maintain cooperation by reputation

Reputation formation is a key to understanding indirect reciprocity. In particular, the way to assign reputation to each individual, namely a norm that describes who is good and who is bad, greatly affects the possibility of sustained cooperation in the population. Previously, we have exhaustively studied reputation dynamics that are able to maintain a high level of cooperation at the ESS. However, this analysis examined the stability of monomorphic population and did not investigate polymorphic population where several strategies coexist. Here, we study the evolutionary dynamics of multiple behavioral strategies by replicator dynamics. We exhaustively study all 16 possible norms under which the reputation of a player in the next round is determined by the action of the self and the reputation of the opponent. For each norm, we explore evolutionary dynamics of three strategies: unconditional cooperators, unconditional defectors, and conditional cooperators. We find that only three norms, simple-standing, Kandori, and shunning, can make conditional cooperation evolutionarily stable, hence, realize sustained cooperation. The other 13 norms, including scoring, ultimately lead to the invasion by defectors. Also, we study the model in which private reputation errors exist to a small extent. In this case, we find the stable coexistence of unconditional and conditional cooperators under the three norms.     

Complex transition to cooperative behavior in a structured population model

Cooperation plays an important role in the evolution of species and human societies. The understanding of the emergence and persistence of cooperation in those systems is a fascinating and fundamental question. Many mechanisms were extensively studied and proposed as supporting cooperation. The current work addresses the role of migration for the maintenance of cooperation in structured populations. This problem is investigated in an evolutionary perspective through the prisoner's dilemma game paradigm. It is found that migration and structure play an essential role in the evolution of the cooperative behavior. The possible outcomes of the model are extinction of the entire population, dominance of the cooperative strategy and coexistence between cooperators and defectors. The coexistence phase is obtained in the range of large migration rates. It is also verified the existence of a critical level of structuring beyond that cooperation is always likely. In resume, we conclude that the increase in the number of demes as well as in the migration rate favor the fixation of the cooperative behavior.     

A multi‐perspective view of genetic variation in Cameroon

In this study, we report the genetic variation of autosomal and Y‐chromosomal microsatellites in a large Cameroon population dataset (a total of 11 populations) and jointly analyze novel and previous genetic data (mitochondrial DNA and protein coding loci) taking geographic and cultural factors into consideration. The complex pattern of genetic variation of Cameroon can in part be described by contrasting two geographic areas (corresponding to the northern and southern part of the country), which differ substantially in environmental, biological, and cultural aspects. Northern Cameroon populations show a greater within‐ and among‐group diversity, a finding that reflects the complex migratory patterns and the linguistic heterogeneity of this area. A striking reduction of Y‐chromosomal genetic diversity was observed in some populations of the northern part of the country (Podokwo and Uldeme), a result that seems to be related to their demographic history rather than to sampling issues. By exploring patterns of genetic, geographic, and linguistic variation, we detect a preferential correlation between genetics and geography for mtDNA. This finding could reflect a female matrimonial mobility that is less constrained by linguistic factors than in males. Finally, we apply the island model to mitochondrial and Y‐chromosomal data and obtain a female‐to‐male migration Nν ratio that was more than double in the northern part of the country. The combined effect of the propensity to inter‐populational admixture of females, favored by cultural contacts, and of genetic drift acting on Y‐chromosomal diversity could account for the peculiar genetic pattern observed in northern Cameroon. Am J Phys Anthropol, 2009. © 2009 Wiley‐Liss, Inc.     

Genetic differentiation and the evolution of cooperation in chimpanzees and humans

It has been proposed that human cooperation is unique among animals for its scale and complexity, its altruistic nature and its occurrence among large groups of individuals that are not closely related or are even strangers. One potential solution to this puzzle is that the unique aspects of human cooperation evolved as a result of high levels of lethal competition (i.e. warfare) between genetically differentiated groups. Although between-group migration would seem to make this scenario unlikely, the plausibility of the between-group competition model has recently been supported by analyses using estimates of genetic differentiation derived from contemporary human groups hypothesized to be representative of those that existed during the time period when human cooperation evolved. Here, we examine levels of between-group genetic differentiation in a large sample of contemporary human groups selected to overcome some of the problems with earlier estimates, and compare them with those of chimpanzees. We find that our estimates of between-group genetic differentiation in contemporary humans are lower than those used in previous tests, and not higher than those of chimpanzees. Because levels of between-group competition in contemporary humans and chimpanzees are also similar, these findings suggest that the identification of other factors that differ between chimpanzees and humans may be needed to provide a compelling explanation of why humans, but not chimpanzees, display the unique features of human cooperation.     

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.     

Reduction of Supercritical Multiregional Stochastic Models with Fast Migration

In this work we study the behavior of a time discrete multiregional stochastic model for a population structured in age classes and spread out in different spatial patches between which individuals can migrate. The dynamics of the population is controlled both by reproduction-survival and by migration. These processes take place at different time scales in the sense of the latter being much faster than the former. We incorporate the effect of demographic stochasticity into the population, which results in both dynamics being modelled by multitype Bienaymé–Galton–Watson branching processes. We present a multitype global model that incorporates the effect of both processes and, making use of the existence of different time scales for demography and migration, build a reduced model in which the variables correspond to the total population in each age class. We extend previous results that relate the behavior of the original and the reduced model showing that, given a large enough separation of time scales between demography and migration, we can obtain information about the behavior of the multitype global model through the study of the simpler reduced model. We concentrate on the case where the two systems are supercritical and therefore the expected number of individuals grows to infinity, and show that we can approximate the asymptotic structure of the population vector and the asymptotic population size of the original system through the study of the reduced model.     

Theory of gel electrophoresis of DNA

A theory of the electrophoresis of DNA through gels with large interfiber spacing, such as dilute agarose, is presented. We assume that the DNA molecule moves along its axis through a “tube” in a neutral gel under the influence of the electric field. The tube is random except for possible bias due to the effects of the field. When the field is small, we easily recover the inverse-length dependence of the mobility found previously by de Gennes and by Doi and Edwards. At higher fields, a new effect appears; the tube becomes oriented because the field biases the direction of the leading end of the chain as it moves to form an extension of the tube. This leads to an increase of the mobility with increasing field by adding a field-dependent but length-independent term to the mobility expression. In agreement with experiment, we find that the field effect can be important at fields as low as 1 V/cm and that the effect can seriously decrease the sensitivity of the mobility to chain length. We also examine the fluctuation of the migration distance, the degree of orientation induced by the field, and the transient effects occurring when the feld direction is rotated by a right angle.     

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.     

The evolution of cooperation by the Hankshaw effect

The evolution of cooperation—costly behavior that benefits others—faces one clear obstacle. Namely, cooperators are always at a competitive disadvantage relative to defectors, individuals that reap the benefits, but evade the cost of cooperation. One solution to this problem involves genetic hitchhiking, where the allele encoding cooperation becomes linked to a beneficial mutation, allowing cooperation to rise in abundance. Here, we explore hitchhiking in the context of adaptation to a stressful environment by cooperators and defectors with spatially limited dispersal. Under such conditions, clustered cooperators reach higher local densities, thereby experiencing more mutational opportunities than defectors. Thus, the allele encoding cooperation has a greater probability of hitchhiking with alleles conferring stress adaptation. We label this probabilistic enhancement the “Hankshaw effect” after the character Sissy Hankshaw, whose anomalously large thumbs made her a singularly effective hitchhiker. Using an agent‐based model, we reveal a broad set of conditions that allow the evolution of cooperation through this effect. Additionally, we show that spite, a costly behavior that harms others, can evolve by the Hankshaw effect. While in an unchanging environment these costly social behaviors have transient success, in a dynamic environment, cooperation and spite can persist indefinitely.     

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.     

Cooperation and the scale of competition in humans

Explaining cooperation is one of the greatest challenges for evolutionary biology. It is particularly a problem in species such as humans, where there is cooperation between nonrelatives. Numerous possible solutions have been suggested for the problem of cooperation between nonrelatives, including punishment, policing, and various forms of reciprocity. Here, we suggest that local competition for resources can pose a problem for these hypotheses, analogous to how it can select against cooperation between relatives. We extend the prisoner's dilemma (PD) game to show that local competition between interacting individuals can reduce selection for cooperation between nonrelatives. This is because, with local competition, fitness is relative to social partners, and cooperation benefits social partners. We then test whether nonrelated humans adjust their level of cooperation facultatively in response to the scale of competition when playing the PD for cash prizes. As predicted, we found that individuals were less likely to cooperate when competition was relatively local. Cooperation between humans will therefore be most likely when repeated interactions take place on a local scale between small numbers of people, and competition for resources takes place on a more global scale among large numbers of people.     

Social Norms of Cooperation in Small-Scale Societies

Indirect reciprocity, besides providing a convenient framework to address the evolution of moral systems, offers a simple and plausible explanation for the prevalence of cooperation among unrelated individuals. By helping someone, an individual may increase her/his reputation, which may change the pre-disposition of others to help her/him in the future. This, however, depends on what is reckoned as a good or a bad action, i.e., on the adopted social norm responsible for raising or damaging a reputation. In particular, it remains an open question which social norms are able to foster cooperation in small-scale societies, while enduring the wide plethora of stochastic affects inherent to finite populations. Here we address this problem by studying the stochastic dynamics of cooperation under distinct social norms, showing that the leading norms capable of promoting cooperation depend on the community size. However, only a single norm systematically leads to the highest cooperative standards in small communities. That simple norm dictates that only whoever cooperates with good individuals, and defects against bad ones, deserves a good reputation, a pattern that proves robust to errors, mutations and variations in the intensity of selection.     

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.     

Movement patterns, social dynamics, and the evolution of cooperation

The structure of social interactions influences many aspects of social life, including the spread of information and behavior, and the evolution of social phenotypes. After dispersal, organisms move around throughout their lives, and the patterns of their movement influence their social encounters over the course of their lifespan. Though both space and mobility are known to influence social evolution, there is little analysis of the influence of specific movement patterns on evolutionary dynamics. We explored the effects of random movement strategies on the evolution of cooperation using an agent-based prisoner’s dilemma model with mobile agents. This is the first systematic analysis of a model in which cooperators and defectors can use different random movement strategies, which we chose to fall on a spectrum between highly exploratory and highly restricted in their search tendencies. Because limited dispersal and restrictions to local neighborhood size are known to influence the ability of cooperators to effectively assort, we also assessed the robustness of our findings with respect to dispersal and local capacity constraints. We show that differences in patterns of movement can dramatically influence the likelihood of cooperator success, and that the effects of different movement patterns are sensitive to environmental assumptions about offspring dispersal and local space constraints. Since local interactions implicitly generate dynamic social interaction networks, we also measured the average number of unique and total interactions over a lifetime and considered how these emergent network dynamics helped explain the results. This work extends what is known about mobility and the evolution of cooperation, and also has general implications for social models with randomly moving agents.