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hw110

# hw110 - 14.12 Game Theory Muhamet Yildiz Fall 2010 Homework...

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14.12 Game Theory Muhamet Yildiz Fall 2010 Homework 1 Due on 9/28/2010 (in class) 1. In the following pair of games, for each player, check whether the player’s preferences over lotteries are the same? LMR a 2,-1 1,0 3,-2 b 0,0 1,1 2,0 c 1,-3 2,2 1,4 LM R a 3,-3 0,-1 8,-5 b -1,-1 0,1 3,-1 c 0,-7 3,3 0,7 2. Write the following game in normal form: 3. Alice, Bob, and Caroline are moving into a 3-bedroom apartment (with rooms, named 1, 2, and 3). In this problem we want to help them to select their rooms. Each roommate has a strict preference over the rooms. The roommates simultaneously submit their preferences in an envelope, and then the rooms are allocated according to one of the following mechanisms. For each mechanism, check whether submitting the true preferences is a dominant strategy for each roommate. Mechanism 1 First, Alice gets her top ranked room. Then, Bob gets his top ranked room among the remaining two rooms. Finally, Caroline gets the remaining room. Mechanism 2 Alice, Bob, and Caroline have priority scores 0.3, 0, and -0.3, respec- tively; the priority score of a roommate

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hw110 - 14.12 Game Theory Muhamet Yildiz Fall 2010 Homework...

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