The Research And Application Of The Equilibrium Point Of Bounded Rationality

Individuals in population games are bounded rational.Everyone in this game might make an irrational choice when they choose a strategy,which means that the individual may not choose the optimal strategy.In fact,in order to get a better strategy individuals always adjust their strategy.Hence,it is necessary to consider the bounded rationality in population games.In recent years,the problem of environmental pollution has become a major concern of society for a long time.It is necessary to use population game theory to study the problem of social choices.In this paper,we use population game theory and evolutionary dynamics to study some environmental issues deeply under bounded rationality theory.As is well known,outdoors straw burning is one of the main factors that cause environmental pollution.For the study of the farmer's behavior of straw burning,most previous studies focus that those behaviors are the typical agent model,which leads to the deviation of the government management.The problem of straw burning has these characteristics: a lot of farmers participate in straw burning,different strategy set of different farmer,payoff of each farmer is dependent on his chosen strategy,and the characteristics of the current population strategy distribution.In addition,farmers are short-sighted and mimic others around them.Based on the above,we use population game theory and evolutionary dynamics to study the farmers behaviors in this paper.Specifically,we construct single-population game model from a new perspective of population game.Furthermore,we analyze the behaviors of farmers by a simulation technique,for government management providing the suggestions.In order to illustrate our results in detail,this paper is divided into five chapters and is organized as follows:Chapter 1,by introducing the development history and research status of population game,evolutionary dynamics and straw burning,we give a further statement to the research issue.Chapter 2,the definitions and properties of the basic model of population game and its equilibria are introduced,and we give more explanations to the research problem in a geometric figure and some examples.Chapter 3,by introducing the definitions and properties of bounded rationality and evolutionary dynamics,we give the new model of hybrid dynamics.Chapter 4,we construct a population game model with nonlinear payoff function for the problem of straw burning.Besides,the simulation experiment is done in term of the kinetics of replication,Logit and optimal response dynamics and the model of hybrid dynamics which is newly established.Chapter 5,we summarize the main results of this paper and look forward to the future work.