Asymmetric interaction will facilitate the evolution of cooperation

Explaining the evolution of cooperation remains one of the greatest problems for both biology and social science. The classical theories of cooperation suggest that cooperation equilibrium or evolutionary stable strategy between partners can be maintained through genetic similarity or reciprocity relatedness. These classical theories are based on an assumption that partners interact symmetrically with equal payoffs in a game of cooperation interaction. However, the payoff between partners is usually not equal and therefore they often interact asymmetrically in real cooperative systems. With the Hawk-Dove model, we find that the probability of cooperation between cooperative partners will depend closely on the payoff ratio. The higher the payoff ratio between recipients and cooperative actors, the greater will be the probability of cooperation interaction between involved partners. The greatest probability of conflict between cooperative partners will occur when the payoff between partners is equal. The results show that this asymmetric relationship is one of the key dynamics of the evolution of cooperation, and that pure cooperation strategy (i.e., Nash equilibrium) does not exist in asymmetrical cooperation systems, which well explains the direct conflict observed in almost all of the well documented cooperation systems. The model developed here shows that the cost-to-benefit ratio of cooperation is also negatively correlated with the probability of cooperation interaction. A smaller cost-to-benefit ratio of cooperation might be created by the limited dispersal ability or exit cost of the partners involved, and it will make the punishment of the non-cooperative individuals by the recipient more credible, and therefore make it more possible to maintain stable cooperation interaction.     

Friendship, cliquishness, and the emergence of cooperation

The evolution of cooperation is a central problem in biology and the social sciences. While theoretical work using the iterated prisoner's dilemma (IPD) has shown that cooperation among non-kin can be sustained among reciprocal strategies (i.e. tit-for-tat), these results are sensitive to errors in strategy execution, cyclical invasions by free riders, and the specific ecology of strategies. Moreover, the IPD assumes that a strategy's probability of playing the PD game with other individuals is independent of the decisions made by others. Here, we remove the assumption of independent pairing by studying a more plausible cooperative dilemma in which players can preferentially interact with a limited set of known partners and also deploy longer-term accounting strategies that can counteract the effects of random errors. We show that cooperative strategies readily emerge and persist in a range of noisy environments, with successful cooperative strategies (henceforth, cliquers) maintaining medium-term memories for partners and low thresholds for acceptable cooperation (i.e. forgiveness). The success of these strategies relies on their cliquishness-a propensity to defect with strangers if they already have an adequate number of partners. Notably, this combination of medium-term accounting, forgiveness, and cliquishness fits with empirical studies of friendship and other long-term relationships among humans.     

The evolution of payoff matrices: providing incentives to cooperate

Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is stable against invasions by mutant genotypes that alter the payoffs. To answer this question, we develop a two-tiered framework with goal-oriented dynamics at the behavioural time scale and a diploid population genetic model at the evolutionary time scale. Our results are two-fold: first, we show that the prisoner's dilemma is subject to invasions by mutants that provide incentives for cooperation to their partners, and that the resulting game is a coordination game similar to the hawk-dove game. Second, we find that for a large class of mutants and symmetric games, a stable genetic polymorphism will exist in the locus determining the payoff matrix, resulting in a complex pattern of behavioural diversity in the population. Our results highlight the importance of considering the evolution of payoff matrices to understand the evolution of animal social systems.     

The evolution of reciprocity in sizable groups

Recently, several authors have investigated the evolution of reciprocal altruism using the repeated prisoner's dilemma game. These models suggest that natural selection is likely to favor behavioral strategies leading to reciprocal cooperation when pairs of individuals interact repeatedly in potentially cooperative situations. Using the repeated n-person prisoner's dilemma game, we consider whether reciprocal altruism is also likely to evolve when social interactions involve more individuals. We show that the conditions that allow the evolution of reciprocal cooperation become extremely restrictive as group size increases.     

Moving away from nasty encounters enhances cooperation in ecological prisoner's dilemma game

We study the role of migration in the evolution of cooperation. Individuals spatially located on a square lattice play the prisoner's dilemma game. Dissatisfied players, who have been exploited by defectors, tend to terminate interaction with selfish partners by leaving the current habitats, and explore unknown physical niches available surrounding them. The time scale ratio of game interaction to natural selection governs how many game rounds occur before individuals experience strategy updating. Under local migration and strong selection, simulation results demonstrate that cooperation can be stabilized for a wide range of model parameters, and the slower the natural selection, the more favorable for the emergence of cooperation. Besides, how the selection intensity affects cooperators' evolutionary fate is also investigated. We find that increasing it weakens cooperators' viability at different speeds for different time scale ratios. However, cooperation is greatly improved provided that individuals are offered with enough chance to agglomerate, while cooperation can always establish under weak selection but vanishes under very strong selection whenever individuals have less odds to migrate. Whenever the migration range restriction is removed, the parameter area responsible for the emergence of cooperation is, albeit somewhat compressed, still remarkable, validating the effectiveness of collectively migrating in promoting cooperation.     

Charitable giving as a signal of trustworthiness: Disentangling the signaling benefits of altruistic acts

It has been shown that psychological predispositions to benefit others can motivate human cooperation and the evolution of such social preferences can be explained with kin or multi-level selection models. It has also been shown that cooperation can evolve as a costly signal of an unobservable quality that makes a person more attractive with regard to other types of social interactions. Here we show that if a proportion of individuals with social preferences is maintained in the population through kin or multi-level selection, cooperative acts that are truly altruistic can be a costly signal of social preferences and make altruistic individuals more trustworthy interaction partners in social exchange. In a computerized laboratory experiment, we test whether altruistic behavior in the form of charitable giving is indeed correlated with trustworthiness and whether a charitable donation increases the observing agents' trust in the donor. Our results support these hypotheses and show that, apart from trust, responses to altruistic acts can have a rewarding or outcome-equalizing purpose. Our findings corroborate that the signaling benefits of altruistic acts that accrue in social exchange can ease the conditions for the evolution of social preferences.     

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.     

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.     

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.     

Adaptive Dynamics of Altruistic Cooperation in a Metapopulation: Evolutionary Emergence of Cooperators and Defectors or Evolutionary Suicide?

We investigate the evolution of public goods cooperation in a metapopulation model with small local populations, where altruistic cooperation can evolve due to assortment and kin selection, and the evolutionary emergence of cooperators and defectors via evolutionary branching is possible. Although evolutionary branching of cooperation has recently been demonstrated in the continuous snowdrift game and in another model of public goods cooperation, the required conditions on the cost and benefit functions are rather restrictive, e.g., altruistic cooperation cannot evolve in a defector population. We also observe selection for too low cooperation, such that the whole metapopulation goes extinct and evolutionary suicide occurs. We observed intuitive effects of various parameters on the numerical value of the monomorphic singular strategy. Their effect on the final coexisting cooperator–defector pair is more complex: changes expected to increase cooperation decrease the strategy value of the cooperator. However, at the same time the population size of the cooperator increases enough such that the average strategy does increase. We also extend the theory of structured metapopulation models by presenting a method to calculate the fitness gradient in a general class of metapopulation models, and try to make a connection with the kin selection approach.     

Evolution of interactions and cooperation in the spatial prisoner's dilemma game

We study the evolution of cooperation in the spatial prisoner's dilemma game where players are allowed to establish new interactions with others. By employing a simple coevolutionary rule entailing only two crucial parameters, we find that different selection criteria for the new interaction partners as well as their number vitally affect the outcome of the game. The resolution of the social dilemma is most probable if the selection favors more successful players and if their maximally attainable number is restricted. While the preferential selection of the best players promotes cooperation irrespective of game parametrization, the optimal number of new interactions depends somewhat on the temptation to defect. Our findings reveal that the "making of new friends" may be an important activity for the successful evolution of cooperation, but also that partners must be selected carefully and their number limited.     

Partnership

Individuals are called partners when it is in their best interest to help each other, if by doing so they increase the probability of being together in the future when, for similar reasons, they will continue to help each other. Kinsmen or individuals who often face (hedonic) situations in which helping is the dominating strategy are committed to help each other. Partnership may develop among them since the loss of the other means the loss of a guaranteed helper. Thus, they may be willing to take additional risks to help each other. Partnership may occur among unrelated individuals and with no hedonic situations. Partnership creates bonds between partners which may be much stronger than those between kinsmen; an individual may take more risks for his partner than he will ever take for a kin. Partnership may evolve without the sophistication and memory required for reciprocation altruism. Although kin selection, partnership and reciprocation are likely to appear fused as the causes for altruism, we argue that it may be possible to distinguish between them in some situations. We show that as the partners get older partnership may become less important to them. We also show that like cooperation, and for analogous reasons, malice may evolve among partners so that each will be willing to take additional risks in order to eliminate the other.     

Cooperation prevails when individuals adjust their social ties

Conventional evolutionary game theory predicts that natural selection favours the selfish and strong even though cooperative interactions thrive at all levels of organization in living systems. Recent investigations demonstrated that a limiting factor for the evolution of cooperative interactions is the way in which they are organized, cooperators becoming evolutionarily competitive whenever individuals are constrained to interact with few others along the edges of networks with low average connectivity. Despite this insight, the conundrum of cooperation remains since recent empirical data shows that real networks exhibit typically high average connectivity and associated single-to-broad–scale heterogeneity. Here, a computational model is constructed in which individuals are able to self-organize both their strategy and their social ties throughout evolution, based exclusively on their self-interest. We show that the entangled evolution of individual strategy and network structure constitutes a key mechanism for the sustainability of cooperation in social networks. For a given average connectivity of the population, there is a critical value for the ratio W between the time scales associated with the evolution of strategy and of structure above which cooperators wipe out defectors. Moreover, the emerging social networks exhibit an overall heterogeneity that accounts very well for the diversity of patterns recently found in acquired data on social networks. Finally, heterogeneity is found to become maximal when W reaches its critical value. These results show that simple topological dynamics reflecting the individual capacity for self-organization of social ties can produce realistic networks of high average connectivity with associated single-to-broad–scale heterogeneity. On the other hand, they show that cooperation cannot evolve as a result of “social viscosity” alone in heterogeneous networks with high average connectivity, requiring the additional mechanism of topological co-evolution to ensure the survival of cooperative behaviour.     

Coevolution of trustful buyers and cooperative sellers in the trust game

Many online marketplaces enjoy great success. Buyers and sellers in successful markets carry out cooperative transactions even if they do not know each other in advance and a moral hazard exists. An indispensable component that enables cooperation in such social dilemma situations is the reputation system. Under the reputation system, a buyer can avoid transacting with a seller with a bad reputation. A transaction in online marketplaces is better modeled by the trust game than other social dilemma games, including the donation game and the prisoner's dilemma. In addition, most individuals participate mostly as buyers or sellers; each individual does not play the two roles with equal probability. Although the reputation mechanism is known to be able to remove the moral hazard in games with asymmetric roles, competition between different strategies and population dynamics of such a game are not sufficiently understood. On the other hand, existing models of reputation-based cooperation, also known as indirect reciprocity, are based on the symmetric donation game. We analyze the trust game with two fixed roles, where trustees (i.e., sellers) but not investors (i.e., buyers) possess reputation scores. We study the equilibria and the replicator dynamics of the game. We show that the reputation mechanism enables cooperation between unacquainted buyers and sellers under fairly generous conditions, even when such a cooperative equilibrium coexists with an asocial equilibrium in which buyers do not buy and sellers cheat. In addition, we show that not many buyers may care about the seller's reputation under cooperative equilibrium. Buyers' trusting behavior and sellers' reputation-driven cooperative behavior coevolve to alleviate the social dilemma.     

The iterated continuous prisoner's dilemma game cannot explain the evolution of interspecific mutualism in unstructured populations

The evolutionionary origin of inter- and intra-specific cooperation among non-related individuals has been a great challenge for biologists for decades. Recently, the continuous prisoner's dilemma game has been introduced to study this problem. In function of previous payoffs, individuals can change their cooperative investment iteratively in this model system. Killingback and Doebeli (Am. Nat. 160 (2002) 421-438) have shown analytically that intra-specific cooperation can emerge in this model system from originally non-cooperating individuals living in a non-structured population. However, it is also known from an earlier numerical work that inter-specific cooperation (mutualism) cannot evolve in a very similar model. The only difference here is that cooperation occurs among individuals of different species. Based on the model framework used by Killingback and Doebeli (2002), this Note proves analytically that mutualism indeed cannot emerge in this model system. Since numerical results have revealed that mutualism can evolve in this model system if individuals interact in a spatially structured manner, our work emphasizes indirectly the role of spatial structure of populations in the origin of mutualism.     

I Dare You to Punish Me—Vendettas in Games of Cooperation

Everybody has heard of neighbours, who have been fighting over some minor topic for years. The fight goes back and forth, giving the neighbours a hard time. These kind of reciprocal punishments are known as vendettas and they are a cross-cultural phenomenon. In evolutionary biology, punishment is seen as a mechanism for maintaining cooperative behaviour. However, this notion of punishment excludes vendettas. Vendettas pose a special kind of evolutionary problem: they incur high costs on individuals, i.e. costs of punishing and costs of being punished, without any benefits. Theoretically speaking, punishment should be rare in dyadic relationships and vendettas would not evolve under natural selection. In contrast, punishment is assumed to be more efficient in group environments which then can pave the way for vendettas. Accordingly, we found that under the experimental conditions of a prisoner’s dilemma game, human participants punished only rarely and vendettas are scarce. In contrast, we found that participants retaliated frequently in the group environment of a public goods game. They even engaged in cost-intense vendettas (i.e. continuous retaliation), especially when the first punishment was unjustified or ambiguous. Here, punishment was mainly targeted at defectors in the beginning, but provocations led to mushrooming of counter-punishments. Despite the counter-punishing behaviour, participants were able to enhance cooperation levels in the public goods game. Few participants even seemed to anticipate the outbreak of costly vendettas and delayed their punishment to the last possible moment. Overall, our results highlight the importance of different social environments while studying punishment as a cooperation-enhancing mechanism.     

The evolution of cooperation

Darwin recognized that natural selection could not favor a trait in one species solely for the benefit of another species. The modern, selfish-gene view of the world suggests that cooperation between individuals, whether of the same species or different species, should be especially vulnerable to the evolution of noncooperators. Yet, cooperation is prevalent in nature both within and between species. What special circumstances or mechanisms thus favor cooperation? Currently, evolutionary biology offers a set of disparate explanations, and a general framework for this breadth of models has not emerged. Here, we offer a tripartite structure that links previously disconnected views of cooperation. We distinguish three general models by which cooperation can evolve and be maintained: (i) directed reciprocation--cooperation with individuals who give in return; (ii) shared genes--cooperation with relatives (e.g., kin selection); and (iii) byproduct benefits--cooperation as an incidental consequence of selfish action. Each general model is further subdivided. Several renowned examples of cooperation that have lacked explanation until recently--plant-rhizobium symbioses and bacteria-squid light organs--fit squarely within this framework. Natural systems of cooperation often involve more than one model, and a fruitful direction for future research is to understand how these models interact to maintain cooperation in the long term.     

Long-term social bonds promote cooperation in the iterated Prisoner's Dilemma

Reciprocal altruism, one of the most probable explanations for cooperation among non-kin, has been modelled as a Prisoner''s Dilemma. According to this game, cooperation could evolve when individuals, who expect to play again, use conditional strategies like tit-for-tat or Pavlov. There is evidence that humans use such strategies to achieve mutual cooperation, but most controlled experiments with non-human animals have failed to find cooperation. One reason for this could be that subjects fail to cooperate because they behave as if they were to play only once. To assess this hypothesis, we conducted an experiment with monogamous zebra finches (Taeniopygia guttata) that were tested in a two-choice apparatus, with either their social partner or an experimental opponent of the opposite sex. We found that zebra finches maintained high levels of cooperation in an iterated Prisoner''s Dilemma game only when interacting with their social partner. Although other mechanisms may have contributed to the observed difference between the two treatments, our results support the hypothesis that animals do not systematically give in to the short-term temptation of cheating when long-term benefits exist. Thus, our findings contradict the commonly accepted idea that reciprocal altruism will be rare in non-human animals.     

Microbial Communication,Cooperation and Cheating: Quorum Sensing Drives the Evolution of Cooperation in Bacteria

An increasing body of empirical evidence suggests that cooperation among clone-mates is common in bacteria. Bacterial cooperation may take the form of the excretion of “public goods”: exoproducts such as virulence factors, exoenzymes or components of the matrix in biofilms, to yield significant benefit for individuals joining in the common effort of producing them. Supposedly in order to spare unnecessary costs when the population is too sparse to supply the sufficient exoproduct level, many bacteria have evolved a simple chemical communication system called quorum sensing (QS), to “measure” the population density of clone-mates in their close neighborhood. Cooperation genes are expressed only above a threshold rate of QS signal molecule re-capture, i.e., above the local quorum of cooperators. The cooperative population is exposed to exploitation by cheaters, i.e., mutants who contribute less or nil to the effort but fully enjoy the benefits of cooperation. The communication system is also vulnerable to a different type of cheaters (“Liars”) who may produce the QS signal but not the exoproduct, thus ruining the reliability of the signal. Since there is no reason to assume that such cheaters cannot evolve and invade the populations of honestly signaling cooperators, the empirical fact of the existence of both bacterial cooperation and the associated QS communication system seems puzzling. Using a stochastic cellular automaton approach and allowing mutations in an initially non-cooperating, non-communicating strain we show that both cooperation and the associated communication system can evolve, spread and remain persistent. The QS genes help cooperative behavior to invade the population, and vice versa; cooperation and communication might have evolved synergistically in bacteria. Moreover, in good agreement with the empirical data recently available, this synergism opens up a remarkably rich repertoire of social interactions in which cheating and exploitation are commonplace.     

Kin selection and the Evolution of Mutualisms between Species

Hamilton's theory of kin selection has revolutionized and inspired fifty years of additional theories and experiments on social evolution. Whereas Hamilton's broader intent was to explain the evolutionary stability of cooperation, his focus on shared genetic history appears to have limited the application of his theory to populations within a single species rather than across interacting species. The evolutionary mechanisms for cooperation between species require both spatial and temporal correlations among interacting partners for the benefits to be not only predictable but of sufficient duration to be reliably delivered. As a consequence when the benefits returned by mutualistic partners are redirected to individuals other than the original donor, cooperation usually becomes unstable and parasitism may evolve. However, theoretically, such redirection of mutualistic benefits may actually reinforce, rather than undermine, mutualisms between species when the recipients of these redirected benefits are genetically related to the original donor. Here, I review the few mathematical models that have used Hamilton's theory of kin selection to predict the evolution of mutualisms between species. I go on to examine the applicability of these models to the most well‐studied case of mutualism, pollinating seed predators, where the role of kin selection may have been previously overlooked. Future detailed studies of the direct, and indirect, benefits of mutualism are likely to reveal additional possibilities for applying Hamilton's theory of kin selection to mutualisms between species.