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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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marked as duplicate by Qiaochu Yuan Oct 20 '11 at 3:41

This question was marked as an exact duplicate of an existing question.

Can you solve the case of 2 players? – Gerry Myerson Oct 20 '11 at 3:39

A search:

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This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. – Austin Mohr Dec 12 '12 at 5:45
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. – draks ... Dec 12 '12 at 8:10

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