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

The benefit of A from the auction is the difference between what it values the object and what it paid for it.

Thus, benefit of A = 60 - 55 = $ 5

This solution is not pareto-optimal, since A can sell off the object to B at $60.

Then, in that case, A can actually realise the difference of $5. Thus he would then have 60 + 45 = 105 $

Whereas, for B, the worth of the object is 70, whereas he pays only 60, thus he would then realise the profit of 10 (since 70 + 40 = 110)

This situation is better for both.

Hope this helps.

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