Revenue equivalence
Any two auctions that end up giving the object to the same bidder and leave the lowest possible type with the same payoff raise the same expected revenue.
Any two auctions that end up giving the object to the same bidder and leave the lowest possible type with the same payoff raise the same expected revenue.
Often misread asQuoting it as the general claim that all auctions raise the same revenue, with the assumptions dropped, so it is then thought to be refuted by any real auction where the format plainly mattered.
How to see it
Revenue follows who wins, not who pays what
Two very different selling procedures can raise the same money on average. If both always hand the object to the same bidder, and both leave the bidder with the lowest possible valuation the same expected payoff, then expected revenue matches, because those two facts pin the payments down between them.
The checkIt requires independent private values, risk neutral bidders, symmetry and no budget limits. Break any one of those and the formats separate, which is why real auction design is a live subject.
Try itCompare first price and second price sealed bid with two bidders drawn from the same range and confirm the expected revenue matches. Now make one bidder risk averse and ask which format they would rather face. The two have just come apart.
Know these first
Leads on to
When it stops being true
- risk-neutrality
- independent-private-values
- no-budget-constraints
Easily confused with
Sources
- Vickrey, W. (1961). Journal of Finance 16(1), 8-37.
- Myerson, R. B. (1981). Mathematics of Operations Research 6(1), 58-73.
- Riley, J. G. and Samuelson, W. F. (1981). American Economic Review 71(3), 381-392.
- Krishna, V. (2002). Academic Press.