Question

There are two bidders bidding for one object. Each one’s value of the object is his private information and independent of the other’s, with their values at v1=500 and v2=600. They simultaneously submit their bids b1 and b2. The one with the higher bid wins the auction but pays the loser’s bid (the second highest price). If b2=500, should bidder 1 try to win or lose? and how much should bidder 1 bid?

Answer 1

A bidder will be at optimum if he pays for the object the amount equal to the value he places for the object. Since b2=500 and it is equal to the value of the object for bidder 1(v1=500), bidder 1 should try to win because if he wins, he will have to pay the loser's bid which is equal to the value that he places for the bid. In other words, bidder 1 should try to win because if he wins,he will be able to buy the object at his willingness to pay value.

Bidder 1 should bid any amount greater than 500 because then b1 will be greater than b2=500 and so he will win the auction and will have to pay only b2=500 for the object.