Two buyers bid in an auction for a single object. Each can bid any integer amount from $0 to $10. The two bids are made simultaneously and independently of each other. The buyers' respective values are v1 = 5 and v2 = 10. The bidder with the higher bid wins (obtains the object) and pays the amount of his own bid. However, the bidder who does not win the auction and thus does not get the object is also obliged to pay half of his own bid. In case of a tie in the bids bidder 2 wins.

(a) Specify the best responses to pure strategies for both bidders.

(b) Identify the pure strategy NE of the game.

(c) Find all dominated strategies for each bidder.

(d) Now restrict the possible bids to $4 and $5, and identify all pure and mixed strategy NE in this game.

(This question is from a game theory class)