What is the set of rationalizable strategies for each

Question

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, . . . , 10. The payoffs are determined as follows: First, the average of the players' selections is calculated and denoted a. That is,

a = (s₁ + s₂ + ........ +s₁₀)/10

where s_i denotes player i 's selection, for 1 = 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?