Research On Population Games Based On Uncertain Parameters And Leader-follower Structure

Population games are a newly emerging direction in the game theory,and the relevant theories provide a uniform research framework for strategic interactions among large populations.This dissertation aims to study the equilibria for population games from two aspects of parameter uncertainty and leader-follower structure.There are a total of9 chapters,with the following arrangements:Chapter 1 mainly outlines the research background,research significance,research contents and innovations.Chapter 2 briefly introduces such preliminaries as some basic concepts,main theorems,and important conclusions used in this article,including the basic concepts and properties of topological space and metric space,the continuity and convexity of vectorvalued function,the continuity and relevant results of set-valued mapping,as well as the models of population games and their relevant basic theories.Chapters 3-8 describe the main research contents and conclusions in detail.In Chapter 3,we introduce the uncertain parameters without specified characteristics but in a known valuing range to the population games,and propose a concept of NS equilibria for population games with uncertain parameters;then,with a certain hypothesis about the continuity and convexity of payoff function,we further prove the existence of NS equilibria using two different methods of Ky Fan inequality and Fan-Glicksberg fixed point theorem.In Chapter 4,we further investigate the stability of NS equilibria for population games with uncertain parameters from three different angles of essential stability,bounded rationality and well-posedness.Firstly,by introducing a concept of essential NS equilibria for population games with uncertain parameters,we draw a conclusion about the generic stability of NS equilibria set for the model of population games with uncertain parameters: it is validated using Fort lemma that NS equilibria for most population games with uncertain parameters is stable when the payoff function has perturbation.Secondly,by establishing a bounded rationality model with an abstract rationality function,we study the structural stability and robustness of the model of population games with uncertain parameters under certain hypothetical conditions.Finally,we further analyze the well-posedness of population games with uncertain parameters in the above-established bounded rationality framework.In Chapter 5,we further extend the model of single-objective population games with uncertain parameters to the scene where the payoff function has multiple objectives,and then propose a concept of weak Pareto-NS equilibria and demonstrate its existence with Ky Fan inequality.In Chapter 6,from three perspectives of essential stability,bounded rationality and well-posedness,we further study the stability of weak Pareto-NS equilibria for multiobjective population games with uncertain parameters.Firstly,we introduce a concept of essential weak Pareto-NS equilibria through the perturbation of multi-objective payoff function and conclude that weak Pareto-NS equilibria for most multi-objective population games with uncertain parameters are essential in the sense of Baire category.Secondly,we establish a bounded rationality framework for multi-objective population games with uncertain parameters.With this framework,we investigate the structural stability,robustness and well-posedness of multi-objective population games.In Chapter 7,by introducing the idea of leader-follower game in the classic games to the population games and combining the actual situations,we establish two models of leader-follower population games: the model of single-leader-multi-follower population games with one leader and follower populations,and the model of multi-leader-multifollower population-games with one leader population and follower populations.And we propose the concept of equilibria separately for these two models and confirm the existence of equilibria under certain hypothetical conditions.In Chapter 8,at three aspects of essential stability,bounded rationality and wellposedness,we continuously study the stability of equilibria for two models of leaderfollower population games proposed in Chapter 7.Firstly,by constructing a game space separately for two types of leader-follower population games and introducing proper measures,we prove that the equilibrium mappings for two types of leader-follower population games are upper semi-continuous and compact-valued for the constructed game space.Using Fort lemma,we confirm the generic stability of equilibria for two models of leader-follower population games when the payoff function has perturbation.Secondly,by establishing a proper bounded rationality model with an abstract function,we investigate the stability of equilibria with bounded rationality at the perturbation of payoff function.Finally,we further draw a conclusion about the well-posedness of two types of leader-follower population games under the established bounded rationality framework.In Chapter 9,we summarize the major study works in this article and put forward to the subsequent thinking prospect.