2. First Price Auction (Modied)

A rst edition copy of The Tragically Divine is being auctioned o. A, B and C are the only bidders for

the book. A values the copy at vA = $10, B at vB = 20 while C values it at vC = 40. The three must

simultaneously submit one of the following bids, $0; $10; $20; $30; $40. Let the highest bid be denoted by

b. If there are m highest bidders and i is one of them then the payo to i is vi

m b. All others get a payo

of 0.

a) Is each player bidding their own valuation a Nash Equilibrium?

b) Is there a Nash Equilibrium where A is the only highest bidder? If so write down the bids; if not

explain why.

c) State the bids of a Nash Equilibrium that results in only C winning the auction.