Two buyers are bidding against each other in an auction for a painting. Buyer 1 values the painting at 8 million YTL and Buyer 2 values it at 6 million YTL. The rules of the auction are that each buyer i will simultaneously choose a bid b, from the set {0, 1, 2,..., 10} million YTL. The buyer with the highest bid wins the painting and pays a price equal to the second highest bid. If the two bids are equal, each buyer gets the painting with 0.5 probability. The payoffs of the buyers are as follows: for b and b2 in {0, 1, 2, ..., 9, 10} u(b,b) 8-b if b b, 0.5(8b) if b = b, if b b. 0 { uz(b1, b2) 6-b if bb, 0.5(6b) if b = b, 0 if b