First Price Auction with a Common Value

Suppose a rm manufacturing dolls has gone bankrupt and is auctioning o its assets. There are two prospective buyers, labeled 1 and 2. The rules of the auction are: the buyers simultaneously and independently submit sealed bids and the rm gives the merchandise to the highest bidder, who must pay her bid. It is common knowledge that the retailer who obtains the load can resell it for a total of $15,000. Thus if a player wins the auction with a bid bi, then bidder i's payo is $15,000bi. The losing bidder receives a payo of $0. If the bidders make the same bid, the rm ips a coin to determine the winner

a) game in the normal form.

b) What is the Nash equilibrium bid for each bidder? Briey explain why this is an equilibrium