Evolutionary Dynamics Of Cooperation In Group-structured Populations

Complex systems are the systems which are composed of many different kinds of components interacting simultaneously and nonlinearly with each other.Emergence is a typical characteristic of complex systems.It means that a whole complex system can present some properties its components do not possess.For instance,cooperation between selfish individuals is prevalent in nature.Cooperation benefits others at costs to cooperators,then the ubiquity of cooperation seems in conflict with Darwinian philosophy of “survival of the fittest”.Thus,exploring the emergence of cooperation is one of the most challenging topics.Research on the emergence of cooperation and the underlying principle of interactions will be in favor of the design of interaction mechanisms as well as the coordination of the components' behaviors.It thus has important theoretical significance and engineering value for some practical problems in complex systems,such as the coordinated control of swarm robot systems,the formation control of unmanned aerial vehicles,the coordinated control of autonomous underwater vehicles,and the optimal scheduling and configuration in electrical energy systems.Game theory is a key method to capture the interaction between components in complex systems.On the basis,evolutionary game theory has been proposed as a competent theoretical framework to analyze the evolutionary dynamics of complex systems.Considering the ubiquitous grouping phenomenon in complex systems,this thesis will mainly concentrate on the emergence cooperation in group-structured populations based on evolutionary game theory.The main results and contributions of this dissertation are as follows.Firstly,we explore the emergence of parochial altruism in populations comprising multiple groups.We establish an analytic model of two versions where individuals each can either exactly belong to one group or belong to an arbitrary number of groups,and specify the conditions under which parochial altruism is selected by virtue of fixation probability and perturbation method.The groups are marked by visible tags.Individuals' strategy is contingent on interacting partners' group property.Only when the participants sharing common tag(s),they play the prisoner's dilemma game;otherwise they play the punishment game.Parochial altruists cooperate with in-group members and punish out-group ones.The results illustrate that cooperation is promoted by assortment in complex systems without intergroup interactions.Emergence of parochial altruism is promoted by assortment as well as by intergroup conflict.Moreover,the group affiliation has a great impact on the emergence of parochial altruism.Secondly,we investigate the emergence of global cooperation in group-structured populations with local and global migrations.We establish an analytic model where individuals are assigned into groups situated in a one-dimensional regular cycle,and explore the emergence of global cooperation based on perturbation method and coalescent theory.The prisoner's dilemma game is employed to capture the interactions between individuals.An individual's strategy is contingent on the partner's group membership.Global cooperators cooperate with everyone else indiscriminately,while ethnocentrists cooperate with in-group members and defect against out-group members.It is found that global migration can enhance ethnocentrism while has few effect on global cooperation.Interestingly,the enforcement of leadership,under which leaders punish defectors,can facilitate global cooperation such that it accounts for a higher fraction than ethnocentrism in equilibrium state.Thirdly,we analyze the emergence of cooperation in group-interaction structured populations with interaction stochasticity.Uncertainty is a characteristic of complex systems.To explore the effects of uncertainty on cooperation in group-interaction structured populations,we establish an analytic model where individuals play the public goods game stochastically,and specify the condition under which cooperation is advantageous over defection by virtue of the replicator dynamics.Individuals each can opt-out of the public goods game stochastically with a certain probability.The results illustrate that stochastic opting-out has a significant impact on the emergence of cooperation.In general,stochastic opting-out can enhance cooperation as long as the probability to opt-out is less than a threshold;and otherwise the promoting-effect of the population structure on cooperation is hindered even subverted by stochastic opting-out.Finally,we study the emergence of cooperation in populations driven by punishment.We constitute an analytic model where the punishment is classified into pro-and antisocial punishments subject to two distinct patterns: costly centralized and decentralized punishments.Both the prisoner's dilemma game and the peer(pool)punishment game are employed to model the interactions between individuals.Accordingly,we investigate the effects of punishment on cooperation based on embedded Markov chain.The pro-social punishment is defined as incurring a cost to inflict harm on a defector,while the anti-social punishment is the one targeted on cooperators.The results suggest that the pattern of punishment has a great impact on the role of punishment in the evolution of cooperation.In absence of anti-social punishment,the costly centralized pool punishment is more conducive in promoting the emergence of cooperation.Anti-social punishment can subvert the positive role of punishment when anti-and pro-social punishments are in the same pattern.However,driven by centralized pool pro-social punishment,cooperation can be more advantageous than defection even in the presence of decentralized peer anti-social punishment.