中国经济研究管理学及财务知识分析.pptx

Game Theory (Microeconomic Theory (IV))Instructor: Yongqin Wang Email: yongqin_School of Economics, Fudan UniversityDecember, 2004Main Reference: Robert Gibbons,1992: Game Theory for Applied Economists, Princeton University Press Fudenberg and Tirole,1991: Game Theory, MIT Press 1.Static Game of Complete Information1.3 Further Discussion on Nash Equilibrium (NE)1.3.1 NE versus Iterated Elimination of Strict Dominance Strategies Proposition A In the -player normal form game if iterated elimination of strictly dominated strategies eliminates all but the strategies , then these strategies are the unique NE of the game. A Formal Definition of NEIn the n-player normal form the strategies are a NE, if for each player i, is (at least tied for) player i’s best response to the strategies specified for the n-1 other players, Cont’d Proposition B In the -player normal form game if the strategies are a NE, then they survive iterated elimination of strictly dominated strategies. 1.3.2 Existence of NETheorem (Nash, 1950): In the -player normal form game if is finite and is finite for every , then there exist at least one NE, possibly involving mixed strategies.See Fudenberg and Tirole (1991) for a rigorous proof. 1.4 Applications 1.4.1 Cournot ModelTwo firms A and B quantity compete. Inverse demand function They have the same constant marginal cost, and there is no fixed cost. Cont’d Firm A’s problem: Cont’d By symmetry, firm B’s problem.Figure Illustration: Response Function, Tatonnement Process Exercise: what will happens if there are n identical Cournot competing firms? (Convergence to Competitive Equilibrium) 1.4.2 The problem of Commons David Hume (1739): if people respond only to private incentives, public goods will be underprovided and public resources over-utilized. Hardin(1968) : The Tragedy of Commons Cont’dThere are