Problem Set IV Fall 2010 Economics 212 1. The normal form game below is repeated in f nitely. Both players discount payo f streams at the discount factor δ . Consider the following strategies. Play B in the f rst stage, and play B if ( B,B ) or ( C, C ) was played in the previous round, and play C otherwise. 2 AB C A 1 , 15 , 00,0 1B 0 ,54 , 40 , 1C 0 , 01, 0 − 1, − 1 a. For what discount factors will the strategies be a subgame perfect equilibrium? Suppose the stage game in part a is played twice and that the players’ preferences are the undiscounted sum of the stage game payo f s. b. Is there a subgame perfect equilibrium in which both players play A in the f rst stage? c. Is there a Nash equilibrium which is not subgame perfect in which both players play A in the f rst stage? 2. Consider a symmetric Bertrand duopoly problem in which each of two f rms announces a price simultaneously and the f rm that announces the lower price will be able to sell Q =13 − p i and the other f rm sells nothing. There is constant marginal cost of producing the good which is equal to 1 .I
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