Question

Revenue equivalence.

Consider a sealed-bid auction in which the highest-bidder wins and pays the amount that they bid and the lowest bidder receives a payment equal to the difference between the first- and second-highest bids. Why doesn?t this auction pay the seller the same revenue as the four standard auctions? That is, why doesn?t the revenue equivalence theorem apply here?

Thank you.

Answer 1

Revenue equivalence theorem states that under certain conditions, any mechanism that results in same outcome also has the same expected revenue.

In the sealed bid auction the lowest bidder get the amount equal to difference between the first and second highest bid but in revenue equivalence the lowest bidder has an expected payoff of zero. That is why here revenue equivalence theorem cannot be applied. And this is one of the conditions of revenue equivalence theorem.