The Dynamics Research Of Commercial Bank Competition Game Model

With the continuous development and progress of science and technology,nonlinear dynamics also obtained the swift and violent development,especially in the field of applied mathematics emerged a large number of dynamical models which is established from the economics and other fields,of which the oligopoly game model plays a very important role in the oligopoly market competition relationship.This paper for a class of commercial bank by quantity of loans competition in the financial market,analyzed the stability of the duopoly game model with different expectations and limited rational expectations,duopoly game model based on delay,limited rational expectations triopoly game model of fixed point and numerical simulate the complex dynamic behaviors such as bifurcation and chaos.Especially simulated two parameters bifurcation diagrams of the system with two different parameters changing at the same time,and more intuitively reflected the complicated competition between banks,provides the certain reference value for policymakers.In this paper,the main research contents has the following several partsThe first chapter mainly introduces the research background and significance of the thesis,the development process of the game theory and application situation in economics,as well as discrete dynamical system theory and research methods.The second chapter established the commercial bank duopoly game model with different expectations and limited rational expectations respectively.Analyzed the stability of the fixed point by using the stability theory.using center manifold theorem and bifurcation theory strictly proved that the system occur Flip bifurcation condition in the Nash equilibrium.And through numerical simulate bifurcation and chaos of the system and other the complex dynamic behaviors,especially to simulate the system two parameters bifurcation diagrams and single parameter bifurcation diagrams,the maximum Lyapunov exponents diagrams,phase diagrams,chaotic attractor,basin of attraction,and other complex dynamic behavior,qualitative analysis of the dynamic characteristics of the system.The third chapter mainly established the commercial bank with delayed decision-making bounded rationality of duopoly game model,analyzed the influence of delay decision variables are introduced to the system and the influence of the size of the delayed decision variables on the stability of the system.Analyzed the stability of fixed point and through numerical simulate two parameters bifurcation diagrams,the domain of stability of the system,single parameter bifurcation diagrams and maximum Lyapunov exponents diagrams found consider delaying decisions for commercial banks to maintain the stable of financial markets and delay the onset of market volatility.The fourth chapter established a limited rational expectations of commercial bank triopoly game model,theoretical analysis the stability of fixed point of the system,through the numerical simulation of triopoly game model of two parameters of the bifurcation diagrams,single parameter bifurcation diagrams,chaos attractor and other dynamical characteristics,analyzed the complex dynamical behavior of the system.