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【正文】 Game Theory (Microeconomic Theory (IV)) Instructor: Yongqin Wang Email: School of Economics, Fudan University December, 2020 Main Reference: Robert Gibbons,1992: Game Theory for Applied Economists, Princeton University Press Fudenberg and Tirole,1991: Game Theory, MIT Press Game of Complete Information ? Further Discussion on Nash Equilibrium (NE) ? 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. 11{ , . . . , 。 , . . . , }nnG S S u u?n**1( , ..., )nssA Formal Definition of NE ? In the nplayer 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 n1 other players, 11{ , ..., 。 , ..., }nnG S S u u?**1( , ..., )nss*is* * * * * * * * *1 1 1 1 1 1( , . . . , , , , . . . , ) ( , . . . , , , , . . . , )i i i n i i i i ns s s s s u s s s s s? ? ? ??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. 11{ , . . . , 。 , . . . , }nnG S S u u?**1( , ..., )nssn Existence of NE Theorem (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. n11{ , . . . , 。 , . . . , }nnG S S u u?n iS i Applications Cournot Model Two firms A and B quantity pete. Inverse demand function They have the same constant marginal cost, and there is no fixed cost.
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