Second-price sealed bid auction.Suppose n bidders bid for an object for sale.Their commonly known valuations of the objects are v1>v2>...>vn>0,respectively.Each bidder i submits a bid Bi in a sealed evenlope to the seller.The bidder who bids the highest wins and pays the second highest bid.Suppose bidder i wins,then her payoff is then vi-max(j不等于i)Bj.Other bidders'payoffs are all 0.Bidding own valuation,that is ,(B1,B2,...Bn)=(v1,v2...vn),is a Nash equilibrium of this auction.In this equilibrium,bidder 1 wins with bidding v1,pays B2=v2 and gains v1-v2.
Find another Nash equilibrium in which bidder 1 wins and a Nash equilibrium in which bidder 2.