# Game Theory-Rationalizable Strategies [duplicate]

Possible Duplicate:
Set of rationalizable strategies

Consider a guessing game with ten players, numbered $1$ through $10$. Simultaneously and independently, the players select integers between $0$ and $10$. Thus player $i$'s strategy space is $S_i = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$ for $i=1,2,\dots,10$.

The payoffs are determined as follows: First, the average of the players' selections is calculated and denoted $a$. That is, $a=(s_1 +s_2 +\dots+s_{10})/10$, where $s_i$ denotes player $i$’s selection, for $i=1,2,\dots,10$. Then player $i$'s payoff is given by $u_i =(a−i−1)s_i$.

What is the set of rationalizable strategies for each player?

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