Evolutionary Dynamics And Emergence Of Cooperation

In real world,cooperation is conducive to many of the major transitions in evolution since it is an essential prerequisite for the establishment of every new level of organization.The puzzle of why cooperative behavior can overmatch the other rivals among fierce competition perplexes evolutionary biologists and sociologists enduringly.In such a puzzle,collaborative individuals devote to benefit the group as a whole at a cost to themselves.Nevertheless,there is a temptation to free ride,that is,defective individuals reap the benefits of altruism without affording any expense.Therefore,according to basic principles of Darwinian evolution,natural selection is conventionally assumed to favor these hoggish defectors who can maximize their own benefits to survive in the cruel competition.Hence,the paradox arises in how the ubiquitous cooperators surpass the competitive defectors.The theme of how to refrain from egoists and insulate from such dilemma is a great conundrum.The evolutionary game theory provides a powerful mathematical framework in exploring this cooperation conundrum.Consequently,this thesis will concentrate on the emergence of cooperation in structured populations based on evolutionary dynamics,consisting of the following contents:We explore the emergence of cooperation when suboptimal alternatives prevail and establish an evolutionary game model by considering the effects of aspirations.A winstay-lose-shift like rule for strategy updating is proposed.The rule prescribes that if the payoff of the current strategy is greater than the aspiration,the strategy keeps,otherwise the strategy changes.Aspiration updating allows individuals to adjust their expected payoff levels.It is shown that suboptimal alternatives can promote the emergence and persistence of cooperation over a wide range of the temptation to defect.Furthermore,a nontrivial phenomenon is found that cooperators prevail as the temptation increases when temptation is small.The aspirations are stabilized at an intermediate level that can facilitate cooperation most.The obtained results also show that the average level of aspirations decrease as the temptation increases.Furthermore,the variance of aspiration levels is minimized for an intermediate level of temptation.The forming of human social ties tends to be with similar individuals.We concentrate on the emergence of cooperation among heterogeneous populations.A simple model is proposed by considering the impact of interplay between the evolution of strategies and that of social partnerships on cooperation dynamics.Whenever two individuals acquire the rewards by playing prisoner's dilemma game with each other,the friendship(friendship is quantified as the weight of a link)between the two individuals deepens.Individuals can switch off the social ties with the partners who are unfriendly and rewire to similar new ones.Under this partner switching mechanism,population structure is divided into several groups and cooperation can prevail.It is observed that the frequent tendency of partner switching can lead to the enhancement of cooperative behavior under the enormous temptation to defect.Moreover,the influence of discounting the relationship between different individuals is also investigated.Meanwhile,the cooperation prevails when the adjustment of friendships mainly depends on the incomes of selected individuals rather than that of their partners.Finally,it is found that too similar population fail to maximize the cooperation and there exists a moderate similarity that can optimize cooperation.We study the mixture of Ultimatum Game and Dictator Game to investigate the evolution of fairness,departing from the conventional assumption of the same game.By assigning dictators in heterogeneous populations in terms of degree and collective influence of individuals,the proposers with tags of dictator play Dictator Game with their recipients,while the common proposers play Ultimatum Game.Different from the prediction by game theory and evolutionary game theory that the rational proposer leaves next to nothing to the recipient and the recipient accepts,it is found that the evolution of fairness can be promoted by assigning appropriate dictators to hubs with high degree and collective influence,irrespective of the population heterogeneity and without the support of any additional evolutionary mechanisms.We analyze the impact of heterogenous allocation of the chips on the evolution of fairness in the framework of the evolutionary game theory.The proposer has the privilege to offer the amount of the chips and make the allocation resolution to the responder.Interestingly,it is found that fairness prevails when the proposer is courageous enough to offer more chips to unsuccessful opponents.Moreover,we find that an amplifying group interaction enlarges the effects of heterogenous allocation of the chips on the evolution of fairness.Deciding how to allocate resources between interdependent systems is significant to optimize efficiency.We institute a theoretical model to elaborate the effects of heterogeneous contribution,induced by such interdependency,on the evolution of cooperation,through implementing the public goods games on two-layer networks.The corresponding players on different layers try to share a fixed amount of resources as the initial investment properly.The symmetry breaking of investments between players located on different layers is able to either prevent investments from,or extract them out of the deadlock.Results show that a moderate investment heterogeneity is best favorable for the evolution of cooperation,and random allocation of investment bias suppresses the cooperators at a wide range of the investment bias and the enhancement effect.Further studies on time evolution with different initial strategy configurations show that the non-interdependent cooperators along the interface of interdependent cooperators also are an indispensable factor in facilitating cooperative behavior.Our main results are qualitatively unchanged even with diversifying investment bias that is subject to uniform distribution.In the animal world,the competition between individuals belonging to different species for a resource often requires the cooperation of several individuals in groups.We develop a generalization of the Hawk Dove Game for an arbitrary number of agents: the N-person Hawk Dove Game.In this model,doves exemplify the cooperative behavior without intraspecies conflict,while hawks represent the aggressive behavior.In the absence of hawks,doves share the resource equally and avoid conflict,but having hawks around lead to doves escaping without fighting.Conversely,hawks fight for the resource at the cost of getting injured.Nevertheless,if doves are present in sufficient number to expel the hawks,they can aggregate to protect the resource,and thus avoid being plundered by hawks.We derive and numerically solve an exact equation for the evolution of the system in both finite and infinite well-mixed populations,finding the conditions for stable coexistence between both species.Furthermore,by varying the different parameters,we found a scenario of bifurcations that leads the system from dominating hawks and coexistence to bi-stability,multiple interior equilibria and dominating doves.