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# V1 - Ec101(ProfCopic,Fa ll2009,Midterm1,Octob er27 Youha...

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Ec101 (Prof Copic), Fall 2009, Midterm 1, October 27. You have 1h to answer the questions. Each question has exactly one correct answer. Each question has an indication of easy, medium, or hard. There are 2 extra‐credit questions which are both harder than the rest ‐ these are indicated as bonus questions ‐ I suggest you first answer the other questions. (Figures 1 and 2 are on the last page.) Stay calm and do well!

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1. (easy) In the game of the battle of the sexes below, row player is Wife (player 1) and column player is Husband (Player 2). Ballet Boxing Ballet 4,1 0,0 Boxing 0,0 1,3 What are all the Nash equilibria of this game? a. (Ballet,Ballet), (Boxing, Ballet) b. (Ballet,Ballet), (Boxing, Boxing), (1/2 Ballet+ 1/2 Boxing, 1/2 Ballet+ 1/2 Boxing) c. (Ballet,Ballet), (Boxing, Boxing), (3/4 Ballet+ 1/4 Boxing, 1/5 Ballet+ 4/5 Boxing) d. (Ballet,Ballet), (Boxing, Boxing), (4/5 Ballet+ 1/5 Boxing, 1/2 Ballet+ 1/2 Boxing) 2. (easy) Consider the game tree in Figure 1. What is the subgame‐perfect Nash equilibrium of that game? (first entry is the strategy of player 1; the rest is strategy of player 2) a. (L; U|L, d|R) b. (L; D|L, d|R) c. (R; U|L, u|R) d. (R; D|L, u|R) 3. (easy) Is there a NE of the game in Figure 1 which is NOT a subgame‐perfect Nash equilibrium of that game? a. (L; U|L, d|R) ‐ because this is the best that player 1 can do. b. (L; D|L, d|R) – because if one plays R, the threat by player 2 is not credible. c. (R; U|L, u|R) ‐ because player 1 could do better by playing L. d. (R; D|L, u|R) ‐ because player 2 should optimize in every situation.
4. (easy) In a backward induction argument the players a. Believe that the other may be crazy. b. Think that the other player will outsmart them. c. Are sure that the other player will follow through even when his threats are not credible. d. Act on the assumption that the other player would only carry out threats that are credible.

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V1 - Ec101(ProfCopic,Fa ll2009,Midterm1,Octob er27 Youha...

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