Research On Evolutionary Dynamics Of Population Games Influenced By Several Types Of Factors

Population games focus on games between one or even more groups with large numbers of participants and they are often used as an analytical framework for the study of strategic interactions between large-scale individuals.The evolutionary dynamics of population games and their applications to cross-disciplinary problems such as traffic congestion,resource allocation and ecological problems have been a hot topic of research in recent years.This thesis focuses on four representative factors that influence the evolutionary dynamics of population games: time delay effect,mechanism design,stochastic effect and spatial structure,and it explores their effects on the equilibrium points and their evolutionary stability properties.The main contents and innovations of this thesis are as follows:Firstly,considering that time delays often exist in realistic situations,we study discrete multi-time delays imitation dynamics in the context of a two-group,two-strategy hawk-dove game.Based on the definition of three types of evolutionary stable strategies,we concentrate on the types of evolutionary stable strategies to which the unique internal equilibrium point belongs and the conditions under which they are established.The sufficient conditions for asymptotic stability of the internal equilibrium point under special two-time delays are analysed by constructing Lyapunov functions and using matrix inequalities,and are extended to the case of any multi-time delays.Further,the correctness of the theoretical results is checked by numerical simulations.Secondly,to address the fact that hitchhikers in game interactions can evade punishment through disguised behaviour,we establish the evolutionary dynamics of a threestrategy multi-player snowpile game with individual punishment and individual disguised behaviour.Theoretical analysis and numerical simulations yield that the three strategies cannot co-exist in the system in the long run.When a larger disguise cost-benefit ratio,multiplicative(penalty)factor,game group size and smaller cost-benefit ratio tend to inhibit betrayers,the system eventually evolves to a frozen state consisting of cooperators and punishers.Conversely,it disadvantages punishers and the system eventually evolves to an active state consisting of cooperators and betrayers.For comparison,a stochastic dynamics of mutation selection is constructed in a finite population,and the results obtained under the assumption of smaller mutations are consistent with those of an infinite population.Then,due to the time cost of the game from the beginning to the end and many disturbances outside the basic assumptions,we construct the evolutionary dynamics of a stochastic multiplayer snowdrift game with a time cost.The deterministic and stochastic stable equilibria of the game and their existence conditions are investigated under the assumptions of a single threshold and different psychological preferences of the betrayer for the time cost.The results show that stochastic stable equilibrium is a subset of deterministic stable equilibria.Furthermore,cooperation can be enhanced with increasing thresholds,payoffs and time costs;while increases in cluster size and snow shovelling costs inhibit cooperation;and the adjustment factor has a weaker effect on the frequency of eventual cooperation compared to cluster size and thresholds.Finally,using the two-threshold multiplayer snowpile game,we investigate the evolutionary dynamics of infinite sufficiently mixed groups,finite sufficiently mixed groups,and sufficiently large groups under the rule graph.The results show that the evolutionary dynamics of infinitely sufficiently mixed and finitely sufficiently mixed populations behave very similarly,with the finite population having a small internally stable equilibrium,but the difference between the equilibria of the two shrinks as the size of the finite population increases.Even though cooperation in structured populations can be reinforced under weak selection,the effect of reinforcement diminishes as the population size increases.