Study Of The Evolutionary Dynamics Of Cooperation Based On Complex Networks

In recent years, evolutionary dynamics based on complex networks has been a populartopic of nonlinear physics and statistic physics. Evolutionary game theory provides aconvenient and systematical framework for studying the evolution of cooperation inpopulation consist of selfish individuals. An individual’s cooperative behavior benefitsothers in the population, but incurs a cost to itself. According to the fundamental principlesof Darwinian selection, individuals will choose defect in order to maximize their benefits,which is obviously opposite to the widespread cooperative phenomena in real world. Theemergence and maintenance of cooperation in population of selfish individuals becomes afundamental and basic problem.As a powerful tool, complex networks are widely used to characterize the relationshipsamong individuals. The combination of complex networks and evolutionary game theoryhas been attracting increasing focuses in recent decades. We firstly make a briefintroduction of complex networks and evolutionary game theory. And then somemechanisms promoting the emergence and maintenance of cooperation are proposed:1. We develop an extended public goods game model, in which individuals distributetheir contributions based on the groups’ qualities. Namely, the individuals are allowed toincrease their investment to the superior group(s) at the expense of the nasty ones. Thequality of a group is positively correlated with its cooperation level. In numericalsimulations, synchronized stochastic strategy updating rule based on pairwise comparisonfor a fixed noise level are adopted. The results show that high-quality group preferencemechanism can greatly improve cooperation, compared with conventional models. Besides,the system with stronger preference towards high-quality groups performs better.Investigation of wealth distribution at equilibrium reveals that cooperators’ wealthappreciates with the increase of preference degree when cooperators take up the samefraction of the population.2. We propose an extended prisoner’s dilemma game model to study the impact ofrecommended role models on the evolution of cooperation. Individuals are endowed withthe capacity to recommend the ones they imitated in the past to their neighbors for strategyupdating. On the one hand, long range imitations between individuals become possiblewith this recommendation mechanism; on the other hand, the recommendation extends theinfluence range of successful individuals. Numerical simulations show that cooperationcan be improved significantly when recommendation is allowed. 3. We propose a model to study the effect of punishment on the evolution ofcooperation in continuous public goods game, wherein individuals have the traits to punishthe co-players based on social tolerance. We show that a reasonable punishment with auniform tolerance can spur individuals to make more investments. Additionally, for a fixedpunishment cost and a fixed fine, a moderate value of tolerance can result in the bestpromotion of cooperation. Furthermore, we investigate the coevolutionary dynamics ofinvestment and tolerance. We find that the population splits into two branches:high-tolerances individuals who make high investments and low-tolerances individualswho make less investments. A dynamic equilibrium is achieved between these two types ofindividuals. Our work extends punishment to continuous cooperative behaviors and theresults may enhance the understanding of altruistic punishment in the evolution of humancooperation.4. We develop two minimal models to explore coevolutionary dynamics on spatialgame. First, a coevolutionery ultimatum game model is proposed, in which individuals areendowed with the capacity to adjust both their strategy and their social ties. Under strategydynamics, individuals preferentially imitate the strategy of more successful neighbors.Meanwhile, the egoists, whose offers do not satisfy the partners, run the risk of beingdismissed. We find that individuals make fairer offers when they are allowed to switchadverse partnerships. Remarkably, the promotion of fairness by partner rewiring is offset ina certain extent by the emergence of isolated individuals. Second, we propose a model toinvestigate the coevolutionary dynamics in the context of public goods game withasymmetric interactions. Individuals are endowed with the capacity to adjust their strategyand switch the groups they participate in. In particular, the interaction graph is representedby a directed graph, wherein individuals just engage in the public goods games organizedby themselves and by the neighbors they point to. With such setting, if a local individualswitches the groups he participates in, it does not change the groups his neighbors willengage in. Thus, the effect of heterogeneity of interaction times on cooperation is avoided,and we can focus on the effect of the ratio of time scales (the time scale of strategyupdating and the time scale of network dynamic) on the evolution of cooperation.5. We develop a model in which individuals play the role of proposer withprobabilities according to the degree. Specifically, players of three types are considered:(A)a fair or empathetic setting since each agent offers the same reward that it is disposed toaccept;(B) pragmatic, who do not distinguish between the different roles and aim to obtainthe same benefit; and (C) agents whose aspiration levels and offers are independent. We investigate the evolution of altruistic behavior of above pure populations with two differenteffective payoffs: accumulated payoffs and normalized payoffs. It is found that, in differenttypes of individuals, the role assignation mechanism has different impact on the altruismlevel of the system.