A total of 10 players are each choosing a number from 012345

A total of 10 players are each choosing a number from {0,1,2,3,4,5,6,7,8). If a players number equals exactly h;ilf nf the average of the ljnmbers submitted by the other nine players, then she is paid $100; otherwise, she is paid 0. Solve for the strategies that survive the IDSDS.

Solution

Interated Deletion of strictly dominated strategies= given pla yer i\'s pure strategy Si,a mixed strategy for a player i Q1: si---> ( 0,1 ) ia a probability distribution over pure strategies (Denote by Ei the space of player i mixed strategies and E=E1X E2......X En)

A rational player should never play a strictly dominated strategy .

IDSDS & Rationality

X is called common Knowledge (CK) between players AB, if for any i E (AB)
K=1,2,3,/n

IDSDS requirs the following Assumptions

1.players are rational

common knowledge of rationality

players know their payoffs

common knowledge of the structure of the game.

in this example= K = 0+1+2+3+4+5+6+7+8 / 9=