Research On Evolutionary Dynamics Of Cooperation Based On Population Game Models

Cooperation is ubiquitous in nature,and it is a decision-making behavior of individ-uals who need to pay a cost to benefit other individuals.In addition,although cooperative behavior is favourable for collective interests,it damages individual own interests to a cer-tain extent,which leads to the social dilemma of cooperation.Therefore,the emergence and maintenance of cooperative behavior among rational individuals has attracted many scholars' attention.Evolutionary game theory provides an effective theoretical framework for studying the evolutionary dynamics of cooperation.This thesis studies the evolution-ary dynamics of cooperation based on the established population game models.The main contents are shown as follows.First,in order to escape punishment of punishers,individuals may choose disguise behavior during the process of game interactions.This thesis thus introduces individual disguise of defectors into the public goods game with peer punishment.We consider both cases of infinite and finite populations,and explore the evolutionary dynamics of cooper-ation strategy.In infinite populations,we find that although low disguise cost can weaken public cooperation,peer punishment still plays a positive role in promoting the evolu-tion of cooperation,no matter whether second-order punishment is considered or not.In addition,we demonstrate that the larger fine on defectors or the smaller the cost of pun-ishment,the more punishment strategy dominates.Furthermore,in finite populations we reveal that when the second-order punishment is not considered,the punishment strategy does not have evolutionary advantage.Whereas when the second-order punishment is considered,punishment can emerge.Second,in the public goods game with an additional strategy of peer punishment,this thesis proposes the regime of resource allocation with threshold.We assume that if con-tributing resources in the common pool exceed the threshold,the contributing resources will be divided into two parts: the first part will be equally allocated by all the individuals,and the second part will be allocated by all the individuals based on their strategy choices.Otherwise all the contributing resources are equally allocated by all the individuals.This thesis explores whether the introduction of this resource allocation can help to solve the second-order free-riders problem.We find that the second-order free-riders problem can be effectively solved by this regime of resource allocation even when most of contributing resources are equally allocated among individuals.In addition,we find that punishment is the dominant strategy in a broad region of allocation parameters.Third,this thesis studies stochastically stable equilibria in the nonlinear public goods game.Specifically,we consider that only when the number of cooperators in a group ex-ceeds a threshold,group members can obtain the benefit of cooperation,otherwise they obtain nothing.We study the stochastically stable equilibria,and give a sufficient and necessary condition in which there exists a unique stochastically stable equilibrium.In addition,cooperators can coexist with defectors at this stochastically stable equilibrium.Furthermore,numerical calculations show that the frequency of cooperators at the stochas-tically stable equilibrium decreases with increasing the group size,increases with increas-ing the synergy factor,and increases with increasing the threshold value.Finally,this thesis proposes an aspiration-based learning rule: Satisfied-Cooperate,Unsatisfied-Defect.Under weak selection,we explore the conditions in which cooper-ation can evolve in the two-person game.We find that the conditions in which cooper-ation can evolve in infinite well-mixed populations,finite well-mixed populations,and structured populations are identical under weak selection.Furthermore,we take the pris-oner's dilemma game as an example,and find that the obtained numerical calculations and computer simulations supports our theoretical results in different types of population structures.We further find that our aspiration learning rule can effectively solve the prob-lem of the evolution of cooperation in prisoner's dilemma game when it is compared with previous aspiration learning rule: Satisfied-Stay,Unsatisfied-Shift.