Dynamic Cournot Competition Analysis Based On Asymmetric Differential Gam

Differential game is the very complex but also very lively field of research in game theory,in which competing parties make decisions in a process of time continuity,with assumptions such as information structure,uncertainty,and the possibility of prenegotiation.In recent years,differential game has become an important analytical tool in the field of industrial organization.Many of the decisions that firms make in a competitive environment are dynamic in nature: they not only have long-term impacts,but also determine the future environment where the firm will operate.Compared with static game which does not explicitly consider the time dimension,differential game can better reflect the dynamic strategic interaction of the firms.The symmetry hypothesis plays an important role in the application of differential game to the study of firm competition,which greatly simplifies the solution of Nash equilibrium.However,in the real competitive market,asymmetry phenomenon or factors are more common,such as different behaviors of competitive firms,differentiated information,heterogeneous production costs and so on.Asymmetry makes it very difficult to solve the Nash equilibrium of differential games,and it is difficult to break through theoretically so far.Current research also rarely involves solving the Nash equilibrium of asymmetric differential game.This thesis tries to put forward the definition of asymmetric differential game in general sense and focuses on the solving problem of two-player asymmetric differential game.Taking dynamic oligopoly game in industrial organization as a typical application field,the influence of asymmetry(heterogeneity)on the solution and properties of differential game Nash equilibrium under different information structures is investigated.The important feature of dynamic oligopoly game is price stickiness,which is related to many real markets,where the firm can control its level of output,but it takes time for the market price to adjust to the level indicated by the demand function.For differential game with linear quadratic structure and differential game with linear cost and hyperbolic inverse demand,this thesis studies the effects of heterogeneous cost and heterogeneous price stickiness on Nash equilibrium and its properties.The main work of this thesis includes:Firstly,the definitions of symmetric differential game and asymmetric differential game are proposed and two methods for calculating the Nash equilibrium of differential game are discussed.Secondly,this thesis establishes a dynamic Cournot monopoly game model with heterogeneous cost under the framework of linear quadratic differential game.The heterogeneity of cost is characterized by the linear and nonlinear terms of the cost function respectively.Using Pontriagin maximum principle and dynamic programming method,Nash equilibrium with open-loop,closed-loop no-memory and feedback information structures are obtained,and the limiting properties of asymmetric Nash equilibrium are analyzed emphatically.This thesis finds that regardless of the information structures,firm with lower cost have higher equilibrium output.Although heterogeneity of cost leads to different equilibrium outputs and price,the limiting properties of Nash equilibrium is consistent with symmetric case.In particular,the asymmetric feedback Nash equilibrium remains asymptotically stable,which contrary to the assertion in Fershtman,Kamien(1987).Thirdly,this thesis further studies the dynamic Cournot oligopoly game with heterogeneous price stickiness.The heterogeneity of price stickiness is represented by differentiated price adjustment parameters.Using Pontryagin maximum principle,Nash equilibrium with open-loop and closed-loop no-memory information structures are obtained and their properties are analyzed.As the limit case of the above game,this thesis studies the influence of asymmetric behavior on the equilibrium strategy of players.This thesis finds that firm with higher price stickiness(smaller price adjustment parameter)have higher equilibrium output and profit,and vice versa,whether in openloop or closed-loop no-memory information structures.This thesis further studies the limit game when the price adjustment parameter of one player remains unchanged and the price adjustment parameter of another player is infinity,which can be regarded as a dynamic duopoly game with asymmetric behavior,that is,one firm as a farsighted player adopts the current price,while the other firm as a myopic player adopts the static price.This thesis shows that the open-loop Nash equilibrium price of the game is a convex combination of the static Cournot equilibrium price and the first “mixed”equilibrium price,while the closed-loop no-memory equilibrium price is a convex combination of the first “mixed” equilibrium price and the second “mixed” equilibrium price.It is well known that in a symmetric duopoly game with sticky price,the openloop Nash equilibrium price is a convex combination of the static Cournot equilibrium price and the static “competitive” price.Therefore,the results of this thesis demonstrate that the heterogeneity of price stickiness changes the price structure and limiting properties of open-loop and closed-loop no-memory Nash equilibrium.Finally,this thesis establishes an asymmetric dynamic Cournot oligopoly game model with hyperbolic inverse demand.Nash equilibrium with open-loop information under heterogeneous cost and heterogeneous stickiness are obtained and the influence of heterogeneity on the equilibrium properties is studied.It is found that firms with lower cost and heterogeneous stickiness have higher equilibrium output but the nonlinear inverse demand does not change the limiting property of equilibrium.