5. You have to choose a number between 1 and 99. Your payoff is calculated as follows.You are playing against 9 other players.Then your payoff will be1if the number you choose is closer to (23)(the average of the numbers chosen by the rest of the players excluding yourself)than any number chosen by any other player. (If k players choose the closest number, they each get a payoff of 1/k.)0if your number is not the closest.For example, if everyone else chooses 99, (23the average) is 66. If you choose 98 you win and get 1. If you choose 99, you get 1/10.

(a)(5%) What choices are weakly dominated?

(b)(5%) If all weakly dominated strategies in (a) are deleted for every player, what strategies are left?

(c) (5%) Among the strategies that are left, delete all weakly dominated strategies foreach player.

(d) (5%) Continue following this procedure as long as you can. What strategies survive?