Two players simultaneously submit bids for an object which is worth 2. Bids must be chosen from the set {0,1,2,3,4,5}. The highest bidder gets the object, and pays his own bid. The loser pays his bid to the winner. In the event of a tie, each player gets the object with probability 1/2 ; and pays nothing.
(a) Find all pure strategy NE.
(b) Are any strategies weakly or strictly dominated?