Equilibria Selection Of Multi-objective Games And Application

With the great improvement of the material wealth,human’s demands are diversifying;and interaction between people is also becoming more frequent on account of the convenient transportation and internet.Hence,multi-objective game theory has a deepened effect on decision makers.It is well-known that equilibria are a consensus of behaviors among players under the assumption of full rationality.However,due to the complexity of game,the bounded rationality of players,information asymmetry and many other factors,equilibrium is often diverse rather than unique,which seriously hinders the achievement and stability of equilibrium.Unfortunately,multi-objective games extra have conflict among objectives,which makes the achievement and stability of equilibria become more difficult.By bargaining,bounded rationality and dynamic,the dissertation systematically studies the equilibria selection in multi-objective games.The full text consists of eight chapters,each of which is arranged as follows:Chapter 1 mainly summarizes the research background,significance of the topic selection,research content and innovation points of the paper.In Chapter 2,some basic concepts,main theorems and other preliminary knowledge are briefly introduced for better readability.They include the basic concepts,basic properties,continuity and convexity of vector-valued functions in topological and metric spaces,continuity and its main theorems of set-value mapping,multi-objective games and their basic theories,population games and their basic theories,and bounded rationality models and their stability.Chapter 3 to Chapter 7 are the main research contents and conclusions of this dissertation.In Chapter 3,under multi-objective games,we introduce a general mode based on bargaining.This mode claims each player will play a self-bargaining game alone on the preference of multi-objective payoffs before making a decision.We propose a concept of bargaining equilibrium,which helps selecting Pareto-Nash equilibria in multi-objective game.And we also establish a number of special bargaining equilibria for reference.In addition,we also briefly consider the situation where the preference of these players’payoff vector is uncertain.That is,these players’s strategies are affected by some vector components of payoffs in an uncertain way.Notably,based on minimum desire(the status quo of bargaining game),we define a discontinuous mode based on bargaining and bargaining equilibria.By numerical simulation,we find the set of the bargaining equilibria sharply shrinks due to the increase of the minimum desire.In Chapter 4,under multi-objective population games,we firstly define a Pareto evolutionarily stable state(PESS)and Pareto neutrally stable state(PNSS)by invasion.Secondly,we propose some replicator dynamics and projection dynamics related to the bargaining equilibria of the third chapter.Thirdly,we establish local stability of PESS and PNSS under these dynamics via local Lyapunov functions,this contributes to the achievement and stability of equilibrium.Moreover,in multi-objective potential games and multi-objective stable games,we also obtain the stability under these dynamics.In Chapter 5,under population games and multi-objective population games,by the bounded rationality of agents in choosing the strategy,we obtain some corresponding approximate solutions and their approximation theorems.They not only make the approximation process more realistic,but also improve the feasibility theory support of Nash equilibrium and weak Pareto-Nash equilibrium algorithms.By Ekeland’s principle,Chapter 6 investigates the structural stability to bounded rationality of multi-objective games about non-convexity and non-compaction.In Chapter 7,in n-person non-cooperative games,we assume that these players are sociologists instead of economists,scilicet they prefer to the payoffs of other players not the ones of themselves.Then,we define new equilibria based on relative payoff maximization,and investigate the stability of these equilibria by the theoretical method of set-value mapping.In fact,the strategy preference of the players are not only affected by their payoffs,but they are also affected by others’.Thereby,we build a bi-objective game by payoffs and relative payoffs,and use the methods of the previous chapters to analyse ultimatum games,Cournot games and tragedy of the commons.Chapter 8 summarizes the main results of the dissertation and further propose research program.