There are two players i = 1,2. Each player announces a number xi ? {0, 1, 2,...,10}g and the announcement is done simultaneously. The one who says lower number wins. If the player wins, he gets 1$, if he loses, he gets 0. In case of a tie (i.e., both players announce the same number), the dollar is split equally between both players.
(a) Is there a strictly dominated strategy?
(b) Find all pure strategy equilibria.