Two people go to an auction. It\'s a sealed-bid auction, meaning that they put t

Question

Two people go to an auction. It's a sealed-bid auction, meaning that they put their bids in an envelope, the higher bidder gets the prize and pays the amount bid, and the other gets nothing and pays nothing. Ties are broken with a coin flip. In this case, player A values the object at $60 and player B values it at $70. Each brings $100 to the auction. Player A bids $55 and player B, overconfidently, bids $40. So player A wins the object even though A wanted it less than B. Player A goes home with the object and $45, and B goes home with $100. Show that outcome not Pareto-efficient. That is, first calculate A's and B's net benefit from the auction as it happened, and then give another possible outcome of the auction that is better for both

Explanation / Answer

Net benefit for A is {$60(Valued price) -$55(bid price)} = $5

Net benefit for B is $0

Another possible outcome that is best for bothe the players is at Bayesian Nash Equilibrium where each player bids for exactly half his/her value.

A bids $ 30 & B bids $ 35

B wins the bid with a benefit of = $70 -$ 35 = $ 35

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