Compute the rationalizable strategies

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Consider the following version of the beauty contest game. There are n >2 players.Each player i submits a real number xi∈[0,100]. Let ¯xbe the mean of the numbers submitted. Suppose among these n players, there are m players whose payoffs are given by (xi- ¯x)2, where 0< m <n2. These m players would like to write number as faraway from the average as possible. The remaining n-m players have the payoffs given by 200-xi-2 ¯x32. These players would like to write numbers as close to two-thirds of the average as possible (convince yourself this is the case). Assume that it is common knowledge in this game that every player is maximizing his/her own payoff.

(a) Prove that xi∈(0,100) is a strictly dominated strategy for each of the m players.

(b) Compute the set of rationalizable strategies that survive iterated elimination of strictly dominated strategies. You need to figure out the rationalizable strategies of the first m players, and the rationalizable strategies for the remaining n-m players.

(c) Compute the rationalizable strategies whenm= 5 andn= 100?

Reference no: EM133083258

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