Research On Evolutionary Dynamics For Multi-strategies On Networks

Various systems including physical systems,biological systems and chemical systems etc can be taken into the framework of generalized statistical thermodynamics due to the extistence of generalized potential function and generalized drives,which determine the stability and evolution of these systems.Cooperation is ubiquitous in human society,various biological systems and economic systems.Evolutionary game theory provides an effective and powerful theoretical framework for investigating the evolution of cooperation in systems consist of selfish and rational individuals.When all the individuals cooperate,the whole population obtains its maximum benefit.However,for any individual,he fares better if he contributes nothing.According to Darwin's theory of evolution,“survival of the fittest”,cooperation loses its evolutionary superiority owing to its low fitness.Therefore,it is a challenging and significant issue to discover the drive between competition among selfish individuals and omnipresent cooperation behavior,as well as the effects of various drives on the evolution of cooperation.In consideration of the diversity of interactions among individuals in the complex systems,we discuss the impact of some mechanisms proposed in this thesis on the evolution of cooperation in spatial public goods games.The main work and achievements of this dissertation are as follows: 1.The evolutionary of dynamics of Wright—Fisher model is analyzed by potential function.In biological systems,the drives such as selection,mutation and migration are regarded as deterministic forces,while random drift is taken as random force.We first obtain the potential functions under different evolutionary drives,and then we analyze their effects on the evolution of the system.2.The impact of persistent cooperation on the evolutionary of cooperation is discussed in spatial public goods games.A strategy named persistent cooperation is introduced in spatial public goods games,and the way that all the benefit is divided equally among all players in the traditional public goods games is improved.The persistent cooperators will pay a second cost to retrieve the remaining proportion of the total benefit contributed by them.By theoretical analysis and numerical simulations on one-dimensional lattices and square lattices,the evolutionary dynamics of persistent cooperation is obtained,as well as the phase diagram in the stable state for each case.Especially,the fixation probability for each strategy is given on one-dimensional lattice.Comparing to the well-mixed populations,it is found that due to the existence spatial structure-force,persistent cooperators greatly suppresse the spreading of defectors under more relaxed conditions in structured populations.3.The evolution of cooperation is studied in the low-carbon game played in traditional industrial clusters.Under constrains of low-carbon environment,each enterprise pulls his weight to participate the low-carbon economy step by step.Taking the heterogeneity into account,we study the low-carbon game played in the traditional industrial cluster based on the framework of continuous public goods game.We first extend the persistent cooperation mechanism used in discrete strategy space,and define the average level of cooperation in the whole cluster as a measure to the mechanism.Then several mechanisms are developed based on average level of cooperation of the group that an agent belongs to for it to invest in game: even-investment,non-even-investment and preference-investment.Later we study the impacts of different investing mechanisms on the average level of cooperation in low-carbon game.Numerical simulations show that all these investing mechanism can promote the cooperating level.Comparing to even-investment,non-even--investment and preference–investment perform better in promoting the low-carbon cooperation level,especially the preference–investment.The stronger preference an individual has,the higher the average level of cooperation of the whole cluster is.4.The evolutionary stability of mixed-strategy is studied on regular networks of degree k.When facing risk or uncertainty,the assumed rational individuals always expect to maximize their benefit in the game,it would be natural that they play the game with mixed-strategies.Each player is arranged on a vertex of the graph.The edges denote the interactions between two individuals.In the limit of weak selection,we first derive the payoff functions of two mixed-strategies under three different updating rules,named “birth-death”,“death-birth” and “imitation”.Then we obtain the conditions for a strategy being continuously stable strategy(CSS),we also confirm that the equilibrium distribution corresponding to the CSS is neighborhood attracting and strongly uninvadable.Finally we apply our theory to the Prisoner's Dilemma and the Snow-Drift game to obtain possible CSS.Simulations are performed for the two special games and the results are well consistent with the conclusions we made.The results obtained in this dissertation present a new idea for promoting the evolution of cooperation in public goods games.The continuously persistent cooperation mechanism provides a reference in the low-carbon game played in traditional industrial clusters.