The Research Of Bounded Rationality For Population Games And Evolutionary Dynamics

Population games mainly consider interactions among populations consisting of large numbers of individuals,which provides a tractable unified framework for strategic interactions among large populations.Population games can be widely used in various fields such as traffic,network congestion,biological competitions,international relations and externalities and so on.Individuals are always assumed to be rational in game theory and economics,which implies that they are omniscience and omnipotence.This hypothesis is however demanding and unrealistic,especially for population games with numerous individuals.Consequently,it is reasonable to study individuals who are bounded rational.The research of bounded rationality is still a hot issue in game theory and economics.This dissertation studies the bounded rationality for population games in two different ways,one in static equilibrium analysis,the other in evolutionarily dynamic analysis.It is divided into seven chapters.As an introduction,research backgrounds and motivations are stated in Chapter one.Moreover,we briefly summarize the status of research about bounded rationality.In Chapter two,many mathematical preliminaries which we will use in the following chapters are stated,such as openness,closeness,compactness of sets,continuity of set-valued maps,fixed point theorems and variational inequalities.Furthermore,the fundamental theory of functional differential equations and the model of population game are also included.In Chapter three,under the hypothesis of bounded rationality of individuals,we propose different mechanisms of bounded rationality and introduce four refinement concepts of Nash equilibria for population games.Applying an important lemma that Nash equilibria for the perturbed population game are equivalent to solutions for some variational inequality,we are able to prove the existence theorems for the above four refined Nash equilibria.Finally,the relations among the four refined Nash equilibria are illurstrated by some examples.Under perturbations on the payoff functions,we further study the stability of Nash equilibria for population games in Chapter four.The concept of essential Nash equilibria for population games is introduced.Moreover,by defining a metric on the space of population games,we prove that the Nash correspondence is upper semi-continuous.What's more,we prove almost all population games are essential in the sense of Baire categories.Besides,considering that it is always unable to refine the Nash equilibria into a singleton,the essential components are defined in population games and we prove that its existence for generic population games.From Chapter five,we investigate the bounded rationality of individuals from the point of evolutionary dynamics.We propose the replicator dynamics with bounded continuously distributed time delay for a special population game with one population and two strategies.Furthermore,we investigate the dynamical behaviour of our model and numerical examples in the context of Hawk-Dove game are used to justify our results.In Chapter six,we perturb the replicator dynamics with time delay in two ways.As a result,we derive two perturbed time-delayed replicator dynamics and the robust stability for our models are discussed.At the end of this chapter,numerical simulations are used to testify our conclusions.The final chapter summarizes this dissertation and some prospects in research of delayed evolutionary dynamics are stated.