Question:

Suppose that there are three players, 1, 2 and 3, bidding for a single object in a rst price auction. The players value the object at v1 2 v2 = 10 and U3 2 8. For 3' = 1,2, 3, let I), denote player i's bid. The players are free to bid any nonnegative price they so choose. The player with the highest bid wins the object and pays her own bid. Thus, player i's payoff is 1:3: I), if she wins and 0 if she loses. When there is a tie, the winner is the player with the smallest number {e.g., player 2 wins if she ties with player 3). Find all pure strategy Nash equilibria of this game. Justify your