Study Of Evolution Of Cooperation Based On Updating Mechanisms

The evolution of cooperation has attracted widely attention in the last decades.How did the human cooperative behavior evolve has become one of hot issues which are sufficiently challenging.As a new research field developed from the classical game theory,evolutionary game theory has provided a powerful framework for studying the evolution of cooperation.Inspired by the international research interest,some update rules of evolutionary game dynamics have been introduced.Our motivation to study these systems is to explore the evolution of cooperation.The main contributions are as follows:An evolutionary dynamic model with finite population was built in the second chapter.In the population,some individuals have the same update mechanism as that of Moran process,while the other individuals have the same update mechanism as that of Imitation process.We calculate the fixation probability and analyze some concrete cases.In contrast with the results of neutral evolution,the fixation probability of a single cooperator with the same update mechanism as that of Imitation process is higher.Besides,more cooperators with the update mechanism of Imitation process lead to higher fixation probabilities when cooperators'quantity is the same.Additionally,we obtain the balance equations of the conditional fixation time and unconditional fixation time.What these equations are doing is to make numerical sense for all the conditional fixation times of a single cooperator are smaller than the average values of the standard Moran and Imitation process.In addition,the conditional fixation time of a single cooperator with update rule of Moran is larger than that of Imitation rules when the intensity of selection is sufficiently small.The simulation results show that the unconditional fixation time of a cooperator who obtains more information is smaller.A model of stochastic evolutionary game dynamics with finite population was built in the third chapter.It combines the standard Moran and Imitation rules with two strategies cooperation and defection.We obtain the expressions of fixation probabilities and fixation times.The one-third rule which has been found in the frequency dependent Moran process also holds for our model.We obtain the conditions of strategy being an evolutionarily stable strategy in our model,and then make a comparison with the standard Moran process.Besides,the analytical results show that compared with the standard Moran process,fixation occurs with higher probabilities under a prisoner's dilemma game and coordination game,but with lower probabilities under a coexistence game.The simulation result shows that the fixation time in our mixed process is lower than that in the standard Imitation process.In comparison with the standard Moran process,fixation always takes more time on average in spatial populations,regardless of the game.In addition,the fixation time decreases with the growth of the number of neighbors.In the fourth chapter,a model of stochastic evolutionary game dynamics with finite population was built.In this population,some individuals update strategies with aspiration updating,while the other individuals update strategies with imitation updating.In the proposed model,we obtain the expression of the mean fraction of cooperators and analyze some concrete cases.Unlike the standard imitation dynamics,there is always a positive probability to support the formation of cooperation.Moreover,the numerical results indicate that more individuals with aspiration updating lead to higher mean fraction of cooperators with imitation updating,which means the invasion of the individuals with aspiration updating is conductive to promoting the cooperation of individuals with imitation updating.In the fifth chapter,we propose a strategy-updating rule driven by local information,which is called Local process.Unlike the standard Moran process,the Local process does not require global information about the strategic environment.By analyzing the dynamical behavior of the system,we explore how the local information influences the fixation of cooperation in two-player evolutionary games.Under weak selection,the decreasing local information leads to an increase of the fixation probability when natural selection does not favor cooperation replacing defection.In the limit of sufficiently large selection,the analytical results indicate that the fixation probability increases with the decrease of the local information,irrespective of the evolutionary games.