econ398win08hw5sol - plays F if East Coast, plays A if West...

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ECON 398 SOLUTIONS FOR HOMEWORK 5 Professor Ozdenoren a) Firm 1 has 8 strategies, examples are: (Player 1 plays West Coast, plays A if East Coast, plays A if West Coast) or (Player 1 plays West Coast, plays F if East Coast, plays A if West Coast) etc. b) First step is to find the Nash equilibria of the sub-games. The sub-game following East Coast is (again Row is player 1 and Column is player 2): A F A 1,1 -2,0 F 0,-2 -1,1 This game has two pure strategy NE: (A,A) and (F,F). The sub-game following West Coast is: A F A 3,3 -3,2 F 2,-3 -2,-2 This game also has two pure strategy NE: (A,A) and (F,F). The following are all sub-game perfect Nash equilibria of this game: I. (Player 1 plays West Coast, plays A if East Coast, plays A if West Coast; Player 2 plays A if East Coast, plays A if West Coast) II. (Player 1 plays West Coast, plays F if East Coast, plays A if West Coast; Player 2
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Unformatted text preview: plays F if East Coast, plays A if West Coast) III. (Player 1 plays East Coast, plays A if East Coast, plays F if West Coast; Player 2 plays A if East Coast, plays F if West Coast) IV. (Player 1 plays East Coast, plays F if East Coast, plays F if West Coast; Player 2 plays F if East Coast, plays F if West Coast) c) The equilibrium (F,F) in the sub-game after West Coast gives -2 to player 1. Player 1 can do better than this by playing East Coast since the equilibria after East Coast give him either 1 or -1. So if player 1 ever plays West Coast, player 2 should deduce that they will play the equilibrium (A,A). This eliminates those sub-game perfect equilibria that are supported by (F,F) after playing West Coast. These III and IV. So these equilibria are eliminated by forward induction....
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