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Problem_set_7 - 4 In the extensive-form game described...

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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. 2. Consider any 2-by-2 normal form game (for instance, the Prisoner’s Dilemma or the Hawk Dove game). Now suppose this game is played twice. That is first played in period 1. The outcome is observed by both players and then played again in period 2. So what we now have is an extensive-form game. How many strategies does each player have in this two-period extensive form game? 3. In the Centipede game (see Basu, Prelude , p. 31), explain in words why the Nash equilibrium will always terminate at the node (3, 0).
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Unformatted text preview: 4. In the extensive-form game described below (considering only pure strategies) locate (a) all the Nash equilibria and (b) all the subgame perfect equilibria. 2 A B U 0, 0 0, 1 D 1, 0 2, 2 L R 1 w 1 0.5 6 5. Consider the usual Battle of the Sexes , described below. 2 B ’ S ’ B 4, 2 0, 0 S 0, 0 2, 4 Suppose this game is going to be played slightly differently. First, player 1 is allowed to decide if this game will be played simultaneously (action S) or if player 2 will move first and then player 1 (action F). After 1 chooses between S and F, the game Battle is played accordingly. (a) Describe this full game by drawing a game tree. [Do not use any payoff matrix in the tree. That is, display the full tree.] (b) Suppose after player 1 chooses between S and F, player 2 is not told what player 1 has chosen. Describe the full game tree for this game. 2 1...
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