2011 上财 高级微观经济学III 课后习题考试真题解答.pdfVIP

Advanced Microeconomic Theory 3 Fall 2010 Problem Set 1 1. Discrete Hotelling Model: There are two players. Each player i is to choose an integer xi between 0 and 10. The payo§ function of player i is 8 x +x i j if x x 2 i j u (x ; x ) = 0:5 if xi = xj : i i j : x +x 1 i j if x x 2 i j What are the rationalizable strategies of this game? 2. Consider a ìBertrandîlike game. There are two players; each player i is to name an integer xi between x and x. The player i whose number is the smaller receives a payo§ of xi c; the other player gets 0. If both players choose the same number x, then each receives 0:5 (x c). (a) Suppose c = 0:5 and x = 1 and x = 100. Find the set of rationalizable strategies. (b) Suppose c = 0:5 and x = 100 and x = 100. Find the set of rationalizable strategies. (c) Suppose c = 0 and x = 100 and x = 100. Find the set of rationalizable strategies. 3. Suppose we Örst eliminate all weakly dominated strategies in Q2. What would be the set of rationalizable strategies for the remaining strategies in each of the cases in Q2? 1