Research On Evolutionary Game Model And Equilibrium In Heterogeneous Cognitive Population

As an analytical method of strategic decision-making, classical game theory is widelyused in many fields. For the perfectly rational hypothesis is overly strict, the explanationof this theory is great limited. Evolutionary game theory which is developed in recentyears introduces the bounded rationality into game analysis. However, most studies are onthe basis of homogenous behavioral pattern, which means that the behavioral pattern andcognitive ability for every one in the population are identical. The latest research results ofcognitive theory show that the behavioral pattern or cognitive ability of player ininteractive process could be different from the ones of opponent. Therefore, it is necessaryto take into account the behavioral agents’ heterogeneity and introduce heterogeneouscognitive ability into evolutionary game theory to construct evolutionary game model andanalyze its equilbrium in heterogenous cognitive population, which has great significancein theory and application to improve game theory and even economic theory, breaches thecurrent bottleneck of game theory which is deviated from reality.This dissertation extends the hypothesis of bounded rationality in the classical gametheory from “behavioral pattern” to “cognitive ability”, which is based on Simon’s “Intendto be rational, but can only reach limited range”. It constructs models of fictitious play andLogit quantal response dynamic in heterogeneous cognitive population and analyzes theirequilibrium respectively. It mainly explores how the heterogeneity of players’ cognitiveability influences game equilibrium and its stability.The cognitive hierarchy of players in traditional fictitious play is extended in thedissertation, and a new fictitious play model is constructed, in which players are randomlyselected and matched within the mixed cognitive hierarchy population. It analyzes theequilibrium of fictitious play in mixed cognitive hierarchy population and the relationsbetween convergence time and game structure, initial beliefs and distributions of cognitivehierarchies. It focuses on the impact that heterogeneous cognitive ability has on theequilibrium of fictitious play. Results obtained shows: for fictitious play withinheterogeneous cognitive population, belief of high level players about others will convergeto the Nash equilibrium if there is only one of it in2-person symmetric game; when thereare several Nash equilibriums, belief of high level players about others will converge to Nash equilibrium both in coordinative and chicken games and it depends on initial beliefsof players’ choice. The convergence rates do not only relate to the initial beliefs of players’choice of players with different cognitive hierarchy, but also to the game structure.It constructs a general model in which the cognitive hierarchy of players isendogenous and they can strategically choose their cognitive hierarchy, and each player inthe mixed cognitive hierarchy population has a strategic behavior to choose his cognitivehierarchy in the fictitious play. In population with heterogenous cognitive hierarchy fromonly level-0~2the relationship among the subjective expected payoffs of players at eachlevel at any moment is discussed, and how the self-interested players owning differentcognitive gift choose the inference way in different game structures is explored. Then itregards the total social payoff as social welfare function to measure social welfare, andstudies how High level players’ strategic behavior influences social welfare under differentgame structures and initial beliefs. Results obtained shows: there is no strategic choice ofcognitive hierarchy in coordinative game. Every player takes his own reasoning approachas the best; however, the strategic choice of cognitive hierarchy of2-level player couldappear only in some extreme cases.The dissertation explores the characteristic of equilibra in Logit quantal responsedynamic process with asymmetric games. It proofs the conditions on which dynamicprocess has the unique equilibrium (fast selection equilibrium or non-fast selectionequilibrium) in different potential functions. For the game structure with symmetric payoff,the convergence rate of Logit response dynamic and relative upper and lower bounds of itshitting time are explored. And for the game structure with asymmetric payoff, it givessimulations to discuss the convergence of the process.It improves the traditional Logit model by random matching within mixed cognitivehierarchy population. It classifies symmetric games according to the structure of Nashequilibirum and the character of Logit response function. Then it applies numerical analysismethod to identify the differences between the outcome of Logit model and original Logitmodel under bounded cognitive ability, and explores how cognitive diversity influencesthe Logit equilibrium. Results obtained shows: under bounded cognitive hierarchy, whenplayers in population have the same initial beliefs, the equilibrium choices of players withdifferent cognitive hierarchy depend not only on the game structure, but more on players’cognitive ability and initial beliefs. Finally, the dissertation discusses the Logit quantal response dynamic process in themixed cognitive hierarchy population, and provides the general description of Logitresponse dynamic with bounded cognitive ability. The equilibrium existence anduniqueness on Logit response dynamic in the mixed cognitive hierarchy population areanalyzed in symmetric games. What’s more, upper and down bound of the hitting time aregiven.The summary and problems further studied have been put forward at the end.