Moran Process In Evolutionary Games Based On Uncertainty Theory

Evolutionary game dynamics assumes that people have”incomplete rationality”,which makes up for the defects of classical game theory and has become a hot research topic.However,the real-life game environment is full of complexity and uncertainty,and how to analyze the evolutionary game model with uncertainty factors becomes a critical problem in the research.In the analysis of evolutionary game models with exact payoffs,Moran process is an important dynamic updating process in stochastic evolutionary game dynamics.Nevertheless,the payoffs are usually not explicit in the actual evolutionary games.To address this problem,this thesis studies the evolutionary game dynamics of the Moran process with interval payoffs by using the interval number to characterize the uncertainty of evolutionary games.The main research of this thesis is as follows.Firstly,we apply the fuzzy theory to the evolutionary game by studying the Moran process with the interval number.This thesis focuses on the Moran process in evolution-ary games with interval payoffs.Using the g H-difference algorithm of interval numbers and the AE solution of the interval linear equation system,we overcome the dimensional catastrophe problem in the iterative process caused by uncertainty factors and then derive the interval fixation probability under weak selection.Secondly,the interval ranking method based on the possibility-degree is explored for the case where the strategy dominates in the population.On the one hand,it is discussed whether natural selection supports strategies to invade populations and the possibility-degree of support.On the other hand,it is discussed whether natural selection favors one strategy over another and the degree of favorable possibility.Based on the two cases,the definition and conditions of the interval evolutionary equilibrium strategy(IEES_N)are obtained.Further,it is shown that the interval Moran process is a generalization of the classical Moran process.Then,the interval prisoner’s dilemma model is studied using the Moran process in evolutionary games based on uncertainty theory.The evolution of the cooperation strategy and the defection strategy in the group is analyzed,and then whether the cooperation strategy is an interval evolutionary equilibrium strategy is determined in the example.At the same time,Monte Carlo simulation is applied to verify the correctness of the method.Finally,in public health events,the model of enterprise epidemic prevention strate-gies is investigated.Through several examples,the impact of uncertainty in local govern-ment regulation and public monitoring on the choice of enterprise epidemic prevention strategies is examined.Also,the practices that should be adopted by enterprises,govern-ments,and the public to control the spread of epidemics when a public health event occurs are obtained.