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 Si={0,1,2,3,4,5,6,7,8,9,10}, for i= 1, 2, ..., 10. The payoffs are determined as follows: First, the average of the players' selections is calculated and denoted a. That is,

s₁+s₂++s₁₀

a =

10

Where s_i denotes player I's selection, for i=1, 2, ...,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 in this game?