Consider a first-price sealed bid auction of a single object with two bidders j-1,2. Bidder1's valuation is v1=2, and bidder 2's valuation is v2=5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts. In the event of a tie, the object is awarded by a flip of a fair coin.

1. write down this auction as a 2x2 matrix.
2. Eliminate the strictly dominated strategies. Write down the resulting matrix game.
3. An auction is efficient if the good is allocated to the bidder with the highest valuation of the good. What are the Nash equilibria of the game? Are the Nash equilibria efficient?