Upstream reciprocity in heterogeneous networks

Many mechanisms for the emergence and maintenance of altruistic behavior in social dilemma situations have been proposed. Indirect reciprocity is one such mechanism, where other-regarding actions of a player are eventually rewarded by other players with whom the original player has not interacted. The upstream reciprocity (also called generalized indirect reciprocity) is a type of indirect reciprocity and represents the concept that those helped by somebody will help other unspecified players. In spite of the evidence for the enhancement of helping behavior by upstream reciprocity in rats and humans, theoretical support for this mechanism is not strong. In the present study, we numerically investigate upstream reciprocity in heterogeneous contact networks, in which the players generally have different number of neighbors. We show that heterogeneous networks considerably enhance cooperation in a game of upstream reciprocity. In heterogeneous networks, the most generous strategy, by which a player helps a neighbor on being helped and in addition initiates helping behavior, first occupies hubs in a network and then disseminates to other players. The scenario to achieve enhanced altruism resembles that seen in the case of the Prisoner's Dilemma game in heterogeneous networks.     

The evolution of generalized reciprocity on social interaction networks

Generalized reciprocity (help anyone, if helped by someone) is a minimal strategy capable of supporting cooperation between unrelated individuals. Its simplicity makes it an attractive model to explain the evolution of reciprocal altruism in animals that lack the information or cognitive skills needed for other types of reciprocity. Yet, generalized reciprocity is anonymous and thus defenseless against exploitation by defectors. Recognizing that animals hardly ever interact randomly, we investigate whether social network structure can mitigate this vulnerability. Our results show that heterogeneous interaction patterns strongly support the evolution of generalized reciprocity. The future probability of being rewarded for an altruistic act is inversely proportional to the average connectivity of the social network when cooperators are rare. Accordingly, sparse networks are conducive to the invasion of reciprocal altruism. Moreover, the evolutionary stability of cooperation is enhanced by a modular network structure. Communities of reciprocal altruists are protected against exploitation, because modularity increases the mean access time, that is, the average number of steps that it takes for a random walk on the network to reach a defector. Sparseness and community structure are characteristic properties of vertebrate social interaction patterns, as illustrated by network data from natural populations ranging from fish to primates.     

Evolution of direct and indirect reciprocity

Indirect reciprocity (IR) occurs when individuals help those who help others. It is important as a potential explanation for why people might develop cooperative reputations. However, previous models of IR are based on the assumption that individuals never meet again. Yet humans and other animals often interact repeatedly within groups, thereby violating the fundamental basis of these models. Whenever re-meeting can occur, discriminating reciprocators can decide whether to help those who helped others (IR) or those who helped them (direct reciprocity, DR). Here I used simulation models to investigate the conditions in which we can expect the different forms of reciprocity to predominate. I show that IR through image scoring becomes unstable with respect to DR by experience scoring as the probability of re-meeting increases. However, using the standing strategy, which takes into account the context of observed defections, IR can be stable with respect to DR even when individuals interact with few partners many times. The findings are important in showing that IR cannot explain a concern for reputation in typical societies unless reputations provide as reliable a guide to cooperative behaviour as does experience.     

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.     

Participation costs can suppress the evolution of upstream reciprocity

Indirect reciprocity, one of the many mechanisms proposed to explain the evolution of cooperation, is the idea that altruistic actions can be rewarded by third parties. Upstream or generalized reciprocity is one type of indirect reciprocity in which individuals help someone if they have been helped by somebody else in the past. Although empirically found to be at work in humans, the evolution of upstream reciprocity is difficult to explain from a theoretical point of view. A recent model of upstream reciprocity, first proposed by Nowak and Roch (2007) and further analyzed by Iwagami and Masuda (2010), shows that while upstream reciprocity alone does not lead to the evolution of cooperation, it can act in tandem with mechanisms such as network reciprocity and increase the total level of cooperativity in the population. We argue, however, that Nowak and Roch's model systematically leads to non-uniform interaction rates, where more cooperative individuals take part in more games than less cooperative ones. As a result, the critical benefit-to-cost ratios derived under this model in previous studies are not invariant with respect to the addition of participation costs. We show that accounting for these costs can hinder and even suppress the evolution of upstream reciprocity, both for populations with non-random encounters and graph-structured populations.     

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.     

The evolution of strong reciprocity: cooperation in heterogeneous populations

How do human groups maintain a high level of cooperation despite a low level of genetic relatedness among group members? We suggest that many humans have a predisposition to punish those who violate group-beneficial norms, even when this imposes a fitness cost on the punisher. Such altruistic punishment is widely observed to sustain high levels of cooperation in behavioral experiments and in natural settings. We offer a model of cooperation and punishment that we call STRONG RECIPROCITY: where members of a group benefit from mutual adherence to a social norm, strong reciprocators obey the norm and punish its violators, even though as a result they receive lower payoffs than other group members, such as selfish agents who violate the norm and do not punish, and pure cooperators who adhere to the norm but free-ride by never punishing. Our agent-based simulations show that, under assumptions approximating likely human environments over the 100000 years prior to the domestication of animals and plants, the proliferation of strong reciprocators when initially rare is highly likely, and that substantial frequencies of all three behavioral types can be sustained in a population. As a result, high levels of cooperation are sustained. Our results do not require that group members be related or that group extinctions occur.     

Evolution of indirect reciprocity in groups of various sizes and comparison with direct reciprocity

Recently many studies have investigated the evolution of indirect reciprocity through which cooperative action is returned by a third individual, e.g. individual A helped B and then receives help from C. Most studies on indirect reciprocity have presumed that only two individuals take part in a single interaction (group), e.g. A helps B and C helps A. In this paper, we investigate the evolution of indirect reciprocity when more than two individuals take part in a single group, and compare the result with direct reciprocity through which cooperative action is directly returned by the recipient. Our analyses show the following. In the population with discriminating cooperators and unconditional defectors, whether implementation error is included or not, (i) both strategies are evolutionarily stable and the evolution of indirect reciprocity becomes more difficult as group size increases, and (ii) the condition for the evolution of indirect reciprocity under standing reputation criterion where the third individuals distinguish between justified and unjustified defections is more relaxed than that under image scoring reputation criterion in which the third individuals do not distinguish with. Furthermore, in the population that also includes unconditional cooperators, (iii) in the presence of errors in implementation, the discriminating strategy is evolutionarily stable not only under standing but also under image scoring if group size is larger than two. Finally, (iv) in the absence of errors in implementation, the condition for the evolution of direct reciprocity is equivalent to that for the evolution of indirect reciprocity under standing, and, in the presence of errors, the condition for the evolution of direct reciprocity is very close to that for the evolution of indirect reciprocity under image scoring.     

The concepts of asymmetric and symmetric power can help resolve the puzzle of altruistic and cooperative behaviour

Evolutionary theory predicts competition in nature yet altruistic and cooperative behaviour appears to reduce the ability to compete in order to help others compete better. This evolutionary puzzle is usually explained by kin selection where close relatives perform altruistic and cooperative acts to help each other and by reciprocity theory (i.e. direct, indirect and generalized reciprocity) among non‐kin. Here, it is proposed that the concepts of asymmetry and symmetry in power and dominance are critical if we are ever to resolve the puzzle of altruism and cooperation towards non‐kin. Asymmetry in power and dominance is likely to emerge under competition in nature as individuals strive to gain greater access to the scarce resources needed to survive and reproduce successfully. Yet asymmetric power presents serious problems for reciprocity theory in that a dominant individual faces a temptation to cheat in interactions with subordinates that is likely to far outweigh any individual selective benefits gained through reciprocal mechanisms. Furthermore, action taken by subordinates to deter non‐reciprocation by dominants is likely to prove prohibitively costly to their fitness, making successful enforcement of reciprocal mechanisms unlikely. It is also argued here that many apparently puzzling forms of cooperation observed in nature (e.g. cooperative breeding in which unrelated subordinates help dominants to breed) might be best explained by asymmetry in power and dominance. Once it is recognized that individuals in these cooperative interactions are subject to the constraints and opportunities imposed on them by asymmetric power then they can be seen as pursuing a ‘least bad’ strategy to promote individual fitness – one that is nevertheless consistent with evolutionary theory. The concept of symmetric power also provides important insights. It can inhibit reciprocal mechanisms in the sense that symmetric power makes it easier for a cheat to appropriate common resources while incurring fewer penalties. Nevertheless under certain restrictive conditions, symmetric power is seen as likely to promote direct reciprocity through ‘tit for tat’.     

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.     

Questioning the cultural evolution of altruism

The evolutionary foundations of helping among nonkin in humans have been the object of intense debates in the past decades. One thesis has had a prominent influence in this debate: the suggestion that genuine altruism, strictly defined as a form of help that comes at a net fitness cost for the benefactor, might have evolved owing to cultural transmission. The gene–culture coevolution literature is wont to claim that cultural evolution changes the selective pressures that normally act to limit the emergence of altruistic behaviours. This paper aims to recall, however, that cultural transmission yields altruism only to the extent that it relies on maladaptive mechanisms, such as conformist imitation and (in some cases) payoff‐biased transmission. This point is sometimes obscured in the literature by a confusion between genuine altruism, maladaptive by definition, and mutualistic forms of cooperation, that benefit all parties in the long run. Theories of cultural altruism do not lift the selective pressures weighing on strictly altruistic actions; they merely shift the burden of maladaptation from social cognition to cultural transmission.     

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.     

Evolutionary evaluation of reciprocity of connections in the turtle tectofugal visual system

In two turtle species—Emys orbicularis and Testudo horsfieldi—by the method of anterograde and retrograde traicing at the light and electron microscopy level, the existence is proven of direct descending projections from the thalamic nucleus of the tectofugal visual system n. rotunds (Rot) to the optic tectum. After injection of tracers into Rot alone and into Rot with involvement of the tectothalamic tract (Trtth), occasional labeled fibers with varicosities and terminals are revealed predominantly in the deep sublayers of SGFS of the rostral optic tectum, while in the lower amount—in other tectal layers. After the tracer injections into the optic tectum, a few retrogradely labeled neurons were found mainly in the Rot ventral parts and within Trtth. Their localization coincides with that of GABA-immunoreactive cells. Electron microscopy showed the existence of many retrogradely labeled dendrites throughout the whole Rot; a few labeled cell bodies were also present there, some of them being also GABA-immunoreactive. These results allow us to conclude about the existence of reciprocal connections between the optic tectum and Rot in turtles, these connections being able to affect processing of visual information in tectum. We suggest that reciprocity of tectothalamic connections might be the ancestral feature of the vertebrate brain; in the course of amniote evolution the functional significance of this feature can be decreased and even lost in parallel with a rise of the role of direct corticotectal projections.     

Transforming the dilemma

How does natural selection lead to cooperation between competing individuals? The Prisoner's Dilemma captures the essence of this problem. Two players can either cooperate or defect. The payoff for mutual cooperation, R, is greater than the payoff for mutual defection, P. But a defector versus a cooperator receives the highest payoff, T, where as the cooperator obtains the lowest payoff, S. Hence, the Prisoner's Dilemma is defined by the payoff ranking T > R > P > S . In a well‐mixed population, defectors always have a higher expected payoff than cooperators, and therefore natural selection favors defectors. The evolution of cooperation requires specific mechanisms. Here we discuss five mechanisms for the evolution of cooperation: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity (or graph selection). Each mechanism leads to a transformation of the Prisoner's Dilemma payoff matrix. From the transformed matrices, we derive the fundamental conditions for the evolution of cooperation. The transformed matrices can be used in standard frameworks of evolutionary dynamics such as the replicator equation or stochastic processes of game dynamics in finite populations.     

Strong reciprocity, human cooperation, and the enforcement of social norms

This paper provides strong evidence challenging the self-interest assumption that dominates the behavioral sciences and much evolutionary thinking. The evidence indicates that many people have a tendency to voluntarily cooperate, if treated fairly, and to punish noncooperators. We call this behavioral propensity “strong reciprocity” and show empirically that it can lead to almost universal cooperation in circumstances in which purely self-interested behavior would cause a complete breakdown of cooperation. In addition, we show that people are willing to punish those who behaved unfairly towards a third person or who defected in a Prisoner’s Dilemma game with a third person. This suggests that strong reciprocity is a powerful device for the enforcement of social norms involving, for example, food sharing or collective action. Strong reciprocity cannot be rationalized as an adaptive trait by the leading evolutionary theories of human cooperation (in other words, kin selection, reciprocal altruism, indirect reciprocity, and costly signaling theory). However, multilevel selection theories of cultural evolution are consistent with strong reciprocity.     

The return of reciprocity: a psychological approach to the evolution of cooperation

Recent developments in evolutionary game theory argue the superiority of punishment over reciprocity as accounts of large-scale human cooperation. I introduce a distinction between a behavioral and a psychological perspective on reciprocity and punishment to question this view. I examine a narrow and a wide version of a psychological mechanism for reciprocity and conclude that a narrow version is clearly distinguishable from punishment, but inadequate for humans; whereas a wide version is applicable to humans but indistinguishable from punishment. The mechanism for reciprocity in humans emerges as a meta-norm that governs both retaliation and punishment. I make predictions open to empirical investigation to confirm or disconfirm this view.

A new route to the evolution of cooperation

The Prisoner's Dilemma (PD) constitutes a widely used metaphor to investigate problems related to the evolution of cooperation. Whenever evolution takes place in well-mixed populations engaged in single rounds of the PD, cooperators cannot resist invasion by defectors, a feature, which is somewhat alleviated whenever populations are spatially distributed. In both cases the populations are characterized by a homogeneous pattern of connectivity, in which every individual is equivalent, sharing the same number of neighbours. Recently, compelling evidence has been accumulated on the strong heterogeneous nature of the network of contacts between individuals in populations. Here we describe the networks of contacts in terms of graphs and show that heterogeneity provides a new mechanism for cooperation to survive. Specifically, we show that cooperators are capable of exploring the heterogeneity of the population structure to become evolutionary competitive. As a result, cooperation becomes the dominating trait in scale-free networks of contacts in which the few highly connected individuals are directly inter-connected, in this way contributing to self-sustain cooperation.     

Two wrongs don't make a right: the initial viability of different assessment rules in the evolution of indirect reciprocity

Indirect reciprocity models are meant to correspond to simple moral systems, in which individuals assess the interactions of third parties in order to condition their cooperative behavior. Despite the staggering number of possible assessment rules in even the simplest of these models, previous research suggests that only a handful are evolutionarily stable against invasion by free riders. These successful assessment rules fall into two categories, one which positively judges miscreants when they refuse to help other miscreants, the other which does not. Previous research has not, however, demonstrated that all of these rules can invade an asocial population—a requirement for a complete theory of social evolution. Here, I present a general analytical model of indirect reciprocity and show that the class of assessment rules which positively judges a refusal to help scofflaws cannot invade a population of defectors, whereas the other class can. When rare, assessment rules which positively judge a refusal to help bad people produce a poor correlation between reputation and behavior. It is this correlation that generates the assortment crucial in sustaining cooperation through indirect reciprocity. Only assessment rules that require good deeds to achieve a good reputation guarantee a strong correlation between behavior and reputation.     

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.