Problem_Set_7_Solutions - Kaushik Basu Spring 2008 Econ 367...

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Kaushik Basu Spring 2008 Econ 367 Game-Theoretic Methods Problem Set 7 1. Consider the extensive-form game described below. 2 1 1 4 2 1 1 1 A B C D 2 x 2 y L R 1 w (a) Describe this game as a normal-form (or strategic-form) game. (b) Locate all the Nash equilibria (in pure strategies) of this game. Which of these equilibria are subgame perfect? (c) What do you think the players would play in this game? Give a brief (no more than three or four sentences) explanation for your answer. (a) A, C A, D B, C B, D L 2, 2 2, 2 1, 1 1, 1 R 1, 1 4, 1 1, 1 4, 1 (b) The players’ best responses for each player are highlighted. And the pure strategy Nash Equilibria are: {(L, (A,C)), (R, (A,D)), (R, (B,C)), (R, (B,D))} In order to test if a NE is subgame perfect, we must show that the strategies are NE in every possible subgame (even those that will never be reached). The Subgame Perfect Nash Equilibrium is (L, (A,C)) and (R, (A,D)). (c) For this you need to say what you think and why.
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Problem_Set_7_Solutions - Kaushik Basu Spring 2008 Econ 367...

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