Research On Network Game And Its Application

In recent years,network game has attracted the attention of scholars from different fields such as mathematics,finance,internet,communication,economics,etc.It has been widely used in the risk analysis and management of commercial bank network,internet financial services and supervision,the optimal distribution of communication flow,the choice of the optimal route of logistics and other industries.Therefore,the study of network game has not only important academic value,but also strong practical significance.Based on mathematical analysis,probability theory,game theory and stochastic analysis,this paper discusses stochastic variables,degree distribution and game theory.The main work is as follows:In Chapter 1,firstly,we present the research background,significance and current research situation of network game at home and abroad,and the application of network game in commercial bank network and internet finance is briefly introduced,and put forward some subjects we need to study;and secondly,we introduce our main research results and innovation points of this dissertation.In Chapter 2,it is known that the behavior(or decision)of someone in a stochastic social network may be influenced by that of his(or her)friends(or neighbors).We consider two stochastic social network game models(a)and(b)which can be defined respectively by two different utility functions.Some sufficient conditions for the existence of Nash equilibrium(NE)in the two network game models are obtained by analyzing the different effort relation between a player and his(or her)friends(or neighbors).In Chapter 3,we present a generalized dynamically evolving random network and a game model taking place on the evolving network.We show that there exits a high dimensional critical curved surface of the parameters related the probabilities of adding or removing vertices or edges such that the evolving network may exhibit three kinds of degree distributions as the time goes to infinity when the parameters belong to the super-critical,critical and sub-critical curved surfaces,respectively.Some sufficient conditions are given for the existence of Nash equilibrium in the game model on the limiting random network.In Chapter 4,we consider a dynamics model of opinions evolution with multi-step effect in social networks in which people may update their opinions not only according to the information that they receive from their social neighbors(friends),but also by the information they obtain from their neighbors' neighbors'...neighbors.It is shown that the opinions evolution with the multi-step effect can not only become consensus finally,but also the consensus can be accelerated.Moreover,we give several examples to show the consensus convergence rate of the deterministic network model.In Chapter 5,we carry on risk analysis and game research on Commercial Banks Network.Because the leverage ratio of commercial banks plays an important role in the risk of banks,we focus on the leverage ratio as an index to measure the risk of commercial banks.We will leverage as a measure of risk of commercial bank based on all 45 listed commercial Banks in our country in data of 2013-2017,research the influence of the leverage ratio of commercial Banks risk management.Based on the leverage ratio,we establish the evolutionary game model of different strategies among banks in the commercial bank network,and obtain the sufficient conditions for the existence of the evolutionary stable solution.In addition,we also give the evolutionary game model in which banks and regulators adopt different strategies in the network composed of commercial banks and regulators,and obtain sufficient conditions for the existence of evolutionary stable solutions.In Chapter 6,based on the game theory of internet finance,by the perspective of social welfare,we establish a tripartite evolutionary game model with users,internet financial platform and financial regulators as the main body,and analyze the stability of the evolutionary game model.The results show that the strategic choice of the internet financial platform,users and regulators will eventually stabilize to some state,which is related to many factors.The alteration of one factor may cause the overall variation.With other conditions remain unchanged,users will be more inclined to choose the platform,when the risk cost of users is less than social benefits;when the amount of fines is higher,the probability of financial platform choosing compliance operation is also greater.