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.     

Evolutionary escape from the prisoner's dilemma

The classic prisoner's dilemma model of game theory is modified by introducing occasional variations on the options available to players. Mutation and selection of game options reliably change the game matrix, gradually, from a prisoner's dilemma game into a byproduct mutualism one, in which cooperation is stable, and "temptation to defect" is replaced by temptation to cooperate. This result suggests that when there are many different potential ways of interacting, exploring those possibilities may make escape from prisoner's dilemmas a common outcome in the world. A consequence is that persistent prisoner's dilemma structures may be less common than one might otherwise expect.     

Dependency Links Can Hinder the Evolution of Cooperation in the Prisoner’s Dilemma Game on Lattices and Networks

Networks with dependency links are more vulnerable when facing the attacks. Recent research also has demonstrated that the interdependent groups support the spreading of cooperation. We study the prisoner’s dilemma games on spatial networks with dependency links, in which a fraction of individual pairs is selected to depend on each other. The dependency individuals can gain an extra payoff whose value is between the payoff of mutual cooperation and the value of temptation to defect. Thus, this mechanism reflects that the dependency relation is stronger than the relation of ordinary mutual cooperation, but it is not large enough to cause the defection of the dependency pair. We show that the dependence of individuals hinders, promotes and never affects the cooperation on regular ring networks, square lattice, random and scale-free networks, respectively. The results for the square lattice and regular ring networks are demonstrated by the pair approximation.     

Evolution of cooperation driven by reputation-based migration

How cooperation emerges and is stabilized has been a puzzling problem to biologists and sociologists since Darwin. One of the possible answers to this problem lies in the mobility patterns. These mobility patterns in previous works are either random-like or driven by payoff-related properties such as fitness, aspiration, or expectation. Here we address another force which drives us to move from place to place: reputation. To this end, we propose a reputation-based model to explore the effect of migration on cooperation in the contest of the prisoner's dilemma. In this model, individuals earn their reputation scores through previous cooperative behaviors. An individual tends to migrate to a new place if he has a neighborhood of low reputation. We show that cooperation is promoted for relatively large population density and not very large temptation to defect. A higher mobility sensitivity to reputation is always better for cooperation. A longer reputation memory favors cooperation, provided that the corresponding mobility sensitivity to reputation is strong enough. The microscopic perception of the effect of this mechanism is also given. Our results may shed some light on the role played by migration in the emergence and persistence of cooperation.     

Density-dependent cooperation as a mechanism for persistence and coexistence

To overcome stress, such as resource limitation, an organism often needs to successfully mediate competition with other members of its own species. This may favor the evolution of defective traits that are harmful to the species population as a whole, and that may lead to its dilution or even to its extinction (the tragedy of the commons). Here, we show that this phenomenon can be circumvented by cooperation plasticity, in which an individual decides, based on environmental conditions, whether to cooperate or to defect. Specifically, we analyze the evolution of density-dependent cooperation. In our model, the population is spatially subdivided, periodically remixed, and comprises several species. We find that evolution pushes individuals to be more cooperative when their own species is at lower densities, and we show that not only could this cooperation prevent the tragedy of the commons, but it could also facilitate coexistence between many species that compete for the same resource.     

Chimpanzees and children avoid mutual defection in a social dilemma

Cooperation often comes with the temptation to defect and benefit at the cost of others. This tension between cooperation and defection is best captured in social dilemmas like the Prisoner's Dilemma. Adult humans have specific strategies to maintain cooperation during Prisoner's Dilemma interactions. Yet, little is known about the ontogenetic and phylogenetic origins of human decision-making strategies in conflict scenarios. To shed light on this question, we compared the strategies used by chimpanzees and 5-year old children to overcome a social dilemma. In our task, waiting for the partner to act first produced the best results for the subject. Alternatively, they could mutually cooperate and divide the rewards. Our findings indicate that the two species differed substantially in their strategies to solve the task. Chimpanzees became more strategic across the study period by waiting longer to act in the social dilemma. Children developed a more efficient strategy of taking turns to reciprocate their rewards. Moreover, children used specific types of communication to coordinate with their partners. These results suggest that while both species behaved strategically to overcome a conflict situation, only children engaged in active cooperation to solve a social dilemma.     

Spatial Patterns of Prisoner’s Dilemma Game in Metapopulations

Because to defect is the evolutionary stable strategy in the prisoner’s dilemma game (PDG), understanding the mechanism generating and maintaining cooperation in PDG, i.e. the paradox of cooperation, has intrinsic significance for understanding social altruism behaviors. Spatial structure serves as the key to this dilemma. Here, we build the model of spatial PDG under a metapopulation framework: the sub-populations of cooperators and defectors obey the rules in spatial PDG as well as the colonization–extinction process of metapopulations. Using the mean-field approximation and the pair approximation, we obtain the differential equations for the dynamics of occupancy and spatial correlation. Cellular automaton is also built to simulate the spatiotemporal dynamics of the spatial PDG in metapopulations. Join-count statistics are used to measure the spatial correlation as well as the spatial association of the metapopulation. Simulation results show that the distribution is self-organized and that it converges to a static boundary due to the boycotting of cooperators to defectors. Metapopulations can survive even when the colonization rate is lower than the extinction rate due to the compensation of cooperation rewards for extinction debt. With a change of parameters in the model, a metapopulation can consist of pure cooperators, pure defectors, or cooperator–defector coexistence. The necessary condition of cooperation evolution is the local colonization of a metapopulation. The spatial correlation between the cooperators tends to be weaker with the increase in the temptation to defect and the habitat connectivity; yet the spatial correlation between defectors becomes stronger. The relationship between spatial structure and the colonization rate is complicated, especially for cooperators. The metapopulation may undergo a temporary period of prosperity just before the extinction, even while the colonization rate is declining. An erratum to this article can be found at     

How wealth accumulation can promote cooperation

Explaining the emergence and stability of cooperation has been a central challenge in biology, economics and sociology. Unfortunately, the mechanisms known to promote it either require elaborate strategies or hold only under restrictive conditions. Here, we report the emergence, survival, and frequent domination of cooperation in a world characterized by selfishness and a strong temptation to defect, when individuals can accumulate wealth. In particular, we study games with local adaptation such as the prisoner's dilemma, to which we add heterogeneity in payoffs. In our model, agents accumulate wealth and invest some of it in their interactions. The larger the investment, the more can potentially be gained or lost, so that present gains affect future payoffs. We find that cooperation survives for a far wider range of parameters than without wealth accumulation and, even more strikingly, that it often dominates defection. This is in stark contrast to the traditional evolutionary prisoner's dilemma in particular, in which cooperation rarely survives and almost never thrives. With the inequality we introduce, on the contrary, cooperators do better than defectors, even without any strategic behavior or exogenously imposed strategies. These results have important consequences for our understanding of the type of social and economic arrangements that are optimal and efficient.     

Pavlovian Prisoner's Dilemma—Analytical results, the quasi-regular phase and spatio-temporal patterns

The Prisoner's Dilemma (PD) game is applied in several research fields due to the emergence of cooperation among selfish players. In this work the PD is studied in a one-dimensional lattice, where each cell represents a player, which in turn can interact with the neighbors playing the PD (cooperate or defect). The update of states adopts the Pavlovian Evolutionary Strategy (PES) or Darwinian Evolutionary Strategy (DES). Adopting PES, if a player receives a positive payoff greater than his/her aspiration level, he/she keeps the current state, and switches otherwise. Adopting DES, player compares his/her payoff with payoff of opponents. If it is not the highest, he/she copies the state of fittest player, switching the state if it is different of his/her current state. The critical temptation values obtained analytically are reported, and the cluster patterns that emerge from the interactions among the players are shown. Also we defined analytical functions that calculate the maximum/minimum size of defective/cooperative clusters. Also, the parameter space is explored with exhaustive computational simulations, which confirm the analytical results and reinforce that Pavlovian strategy foments cooperation among players. In steady state, system can reach the cooperative or quasi-regular phases, when adopting the PES, and cooperative, defective or chaotic phases, adopting the DES. The new quasi-regular phase occurs when several players switch their states in each round, but the proportion of cooperators does not show significant variation. Additionally, the present work shows that the lowest temptation level (T=1) may be considered a trivial case only for the particular case where the players interact with only one neighbor, otherwise system presents the same features that for higher temptation values.     

Coveting thy neighbors fitness as a means to resolve social dilemmas

In spatial evolutionary games the fitness of each individual is traditionally determined by the payoffs it obtains upon playing the game with its neighbors. Since defection yields the highest individual benefits, the outlook for cooperators is gloomy. While network reciprocity promotes collaborative efforts, chances of averting the impending social decline are slim if the temptation to defect is strong. It is, therefore, of interest to identify viable mechanisms that provide additional support for the evolution of cooperation. Inspired by the fact that the environment may be just as important as inheritance for individual development, we introduce a simple switch that allows a player to either keep its original payoff or use the average payoff of all its neighbors. Depending on which payoff is higher, the influence of either option can be tuned by means of a single parameter. We show that, in general, taking into account the environment promotes cooperation. Yet coveting the fitness of one's neighbors too strongly is not optimal. In fact, cooperation thrives best only if the influence of payoffs obtained in the traditional way is equal to that of the average payoff of the neighborhood. We present results for the prisoner's dilemma and the snowdrift game, for different levels of uncertainty governing the strategy adoption process, and for different neighborhood sizes. Our approach outlines a viable route to increased levels of cooperative behavior in structured populations, but one that requires a thoughtful implementation.     

How is sexual conflict over parental care resolved? A meta‐analysis

Biparental care of offspring is both a form of cooperation and a source of conflict. Parents face a trade‐off between current and future reproduction: caring less for the current brood allows individuals to maintain energy reserves and increase their chances of remating. How can selection maintain biparental care, given this temptation to defect? The answer lies in how parents respond to changes in each other’s effort. Game‐theoretical models predict that biparental care is evolutionarily stable when reduced care by one parent leads its partner to increase care, but not so much that it completely compensates for the lost input. Experiments designed to reveal responses to reduced partner effort have mainly focused on birds. We present a meta‐analysis of 54 such studies, and conclude that the mean response was indeed partial compensation. Males and females responded differently and this was in part mediated by the type of manipulation used.     

Resolving the iterated prisoner's dilemma: theory and reality

Pairs of unrelated individuals face a prisoner's dilemma if cooperation is the best mutual outcome, but each player does best to defect regardless of his partner's behaviour. Although mutual defection is the only evolutionarily stable strategy in one-shot games, cooperative solutions based on reciprocity can emerge in iterated games. Among the most prominent theoretical solutions are the so-called bookkeeping strategies, such as tit-for-tat, where individuals copy their partner's behaviour in the previous round. However, the lack of empirical data conforming to predicted strategies has prompted the suggestion that the iterated prisoner's dilemma (IPD) is neither a useful nor realistic basis for investigating cooperation. Here, we discuss several recent studies where authors have used the IPD framework to interpret their data. We evaluate the validity of their approach and highlight the diversity of proposed solutions. Strategies based on precise accounting are relatively uncommon, perhaps because the full set of assumptions of the IPD model are rarely satisfied. Instead, animals use a diverse array of strategies that apparently promote cooperation, despite the temptation to cheat. These include both positive and negative reciprocity, as well as long-term mutual investments based on 'friendships'. Although there are various gaps in these studies that remain to be filled, we argue that in most cases, individuals could theoretically benefit from cheating and that cooperation cannot therefore be explained with the concept of positive pseudo-reciprocity. We suggest that by incorporating empirical data into the theoretical framework, we may gain fundamental new insights into the evolution of mutual reciprocal investment in nature.     

Paleolithic public goods games: why human culture and cooperation did not evolve in one step

It is widely agreed that humans have specific abilities for cooperation and culture that evolved since their split with their last common ancestor with chimpanzees. Many uncertainties remain, however, about the exact moment in the human lineage when these abilities evolved. This article argues that cooperation and culture did not evolve in one step in the human lineage and that the capacity to stick to long-term and risky cooperative arrangements evolved before properly modern culture. I present evidence that Homo heidelbergensis became increasingly able to secure contributions form others in two demanding Paleolithic public good games (PPGGs): cooperative feeding and cooperative breeding. I argue that the temptation to defect is high in these PPGGs and that the evolution of human cooperation in Homo heidelberngensis is best explained by the emergence of modern-like abilities for inhibitory control and goal maintenance. These executive functions are localized in the prefrontal cortex and allow humans to stick to social norms in the face of competing motivations. This scenario is consistent with data on brain evolution that indicate that the largest growth of the prefrontal cortex in human evolution occurred in Homo heidelbergensis and was followed by relative stasis in this part of the brain. One implication of this argument is that subsequent behavioral innovations, including the evolution of symbolism, art, and properly cumulative culture in modern Homo sapiens, are unlikely to be related to a reorganization of the prefrontal cortex, despite frequent claims to the contrary in the literature on the evolution of human culture and cognition.     

A Cooperative System of Two Species with Bidirectional Interactions

Cooperation between species is often regarded to mean that the increase of each species promotes the growth of the other. The well-known cooperative model is the Lotka–Volterra equations (LVEs). In the LVEs, population densities of species increase infinitely as the cooperation is strong, which is called the divergence problem. Moreover, LVEs never exhibit an Allee effect in the case of obligate cooperation. In order to avoid these problems, several models have been established although most of them are rather complex. In this paper, we consider a cooperative system of two species with bidirectional interactions, in which each species also has negative feedback on the other. Population densities of the species will not increase infinitely because of the limited resource and negative feedback. Then, we focus on an extended lattice model of cooperation, which is deduced from reactions on lattice and has the same form as that of LVEs. In the case of obligate cooperation, the model predicts an Allee effect. Global dynamics of the system exhibit essential features of cooperation and basic mechanisms by which the cooperation can lead to coexistence/extinction of species. Intermediate cooperation is shown to be beneficial in cooperation under certain conditions, while extremely strong cooperation is demonstrated to lead to extinction of one/both species. Numerical simulations confirm and extend our results.     

Coevolution of Quantum and Classical Strategies on Evolving Random Networks

We study the coevolution of quantum and classical strategies on weighted and directed random networks in the realm of the prisoner’s dilemma game. During the evolution, agents can break and rewire their links with the aim of maximizing payoffs, and they can also adjust the weights to indicate preferences, either positive or negative, towards their neighbors. The network structure itself is thus also subject to evolution. Importantly, the directionality of links does not affect the accumulation of payoffs nor the strategy transfers, but serves only to designate the owner of each particular link and with it the right to adjust the link as needed. We show that quantum strategies outperform classical strategies, and that the critical temptation to defect at which cooperative behavior can be maintained rises, if the network structure is updated frequently. Punishing neighbors by reducing the weights of their links also plays an important role in maintaining cooperation under adverse conditions. We find that the self-organization of the initially random network structure, driven by the evolutionary competition between quantum and classical strategies, leads to the spontaneous emergence of small average path length and a large clustering coefficient.     

On the strategic stability of monitoring: implications for cooperative wildlife programmes in Africa

Game-theoretic modelling is used to study the design of an agreement among residents to conserve a wildlife resource, by not hunting animals illegally, when the community monitors its own behaviour. The analysis demonstrates that such an agreement may be very much costlier for a government to sustain if its incentive structure avoids the payment of monitoring fees, and instead relies on community benefits for conservation, with bonuses for reporting poachers. Conditions are identified for the agreement to be stable against both the temptation to avoid monitoring and the temptation to poach, either with guns or by snaring. In particular, the size of the community must exceed a critical value. Implications are discussed for community-based wildlife management programmes in Africa.     

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.     

Twin registers across the globe: what's out there in 2002?

Twin research offers the greatest power for the genetic analysis of complex multifactorial traits and diseases in humans. Modern twin analyses extend beyond the classical twin study for estimating the heritability of a trait. The human genome project can fulfil its promises only after functional characterisation of single genes in the context of genetic background and environment. Twin research can make a major contribution in that regard. Twin research is greatly facilitated by the willingness, motivation, cooperation, and generosity of the participants and their families. A second important aspect is the availability of twin registries that serve as a resource for genetic epidemiology. Currently, there is no systematic overview of the twin collections worldwide. This special issue will help to overcome the limited accessibility of this resource by providing basic information on most of the existing twin registers. Furthermore, an additional goal is to facilitate collaboration between registers. Some basic principles, potentials, and problems will be exemplified by my personal experience in the Berlin Twin Study.     

Optimization model of spatial population structure: example of poplar moth laying eggs on leaves

The authors analyze spatial distribution and survival of populations of poplar moth Litchcolletis populifoliella Tr. on its feeding plant--balsam poplar Populus balsamifera. Imago of the moth glue its eggs on the leaves thus determining the future location of their offspring on the host plant. Spatial distribution of eggs on leaf surface and distribution of leaves according egg numbers are not random. On the short distance from each egg the average number of eggs is less, than it should be in case of random distribution. While this distance increases up to some particular value the occurrence of eggs is higher than random. Thus, the eggs of moth are located by groups on the leaf surface. Within each group eggs are situated not very close to each other, this allowing larvae to lower competition for common resource. It is suggested that on the same feeding plant individuals have different interactions: competition, caused by limited quantity of resource and cooperation that is necessary to resist leaf defensive (antibiosis) reaction.     

Neural Correlates of Gender Differences in Reputation Building

Gender differences in cooperative choices and their neural correlates were investigated in a situation where reputation represented a crucial issue. Males and females were involved in an economic exchange (trust game) where economic and reputational payoffs had to be balanced in order to increase personal welfare. At the behavioral level, females showed a stronger reaction to negative reputation judgments that led to higher cooperation than males, measured by back transfers in the game. The neuroanatomical counterpart of this gender difference was found within the reward network (engaged in producing expectations of positive results) and reputation-related brain networks, such as the self-control network (engaged in strategically resisting the temptation to defect) and the mentalizing network (engaged in thinking about how one is viewed by others), in which the dorsolateral prefrontal cortex (DLPFC) and the medial (M)PFC respectively play a crucial role. Furthermore, both DLPFC and MPFC activity correlated with the amount of back transfer, as well as with the personality dimensions assessed with the Big-Five Questionnaire (BFQ-2). Males, according to their greater DLPFC recruitment and their higher level of the BFQ-2 subscale of Dominance, were more focused on implementing a profit-maximizing strategy, pursuing this target irrespectively of others'' judgments. On the contrary, females, according to their greater MPFC activity and their lower level of Dominance, were more focused on the reputation per se and not on the strategic component of reputation building. These findings shed light on the sexual dimorphism related to cooperative behavior and its neural correlates.