Consider an art auction with two bidders in which the auction procedure is that described in the text. Suppose that the auctioneer raises bids by multiples of one thousand dollars starting at the buyer's reservation price of $2,000 and stopping when there is only one bidder left. The Renoir is worth $6,000 to bidder 1 and $7,000 to bidder 2. Each bidder's strategy specifies the maximum that he is willing to bid for the drawing. List all of the strategies available to the two bidders. Suppose that, if the two bidders bid an equal amount, bidder 1 is given the drawing.10 If the bids are unequal, the higher bidder pays the lower bid. Furthermore, the payoffs are as follows: if bidder 1 wins the drawing and pays p dollars for it, then his utility is 6,000 - p, while if bidder 2 wins, his utility is 7,000 - p. Utility to a bidder is zero if he does not win the object.
1. Write down the strategic form of this auction.
2. What would be the strategic form if a coin toss decides the winner when the bids are equal (and a 50% chance of winning implies an expected utility equal to 1/2X utility of winning)?