Optimal auction
The selling rule that maximises the seller's expected revenue rather than social value, typically by holding back the object unless bidding passes a reserve.
Often misread asAssuming the revenue maximising auction is also the efficient one, so the reserve price is read as a safeguard against a silly price rather than as a deliberate sacrifice of worthwhile trades.
How to see it
Revenue is bought by refusing some good trades
A seller who wants money rather than efficiency will not always sell. Setting a reserve price means sometimes keeping the object even though a buyer valued it more than you did, and that deliberate waste is what lifts the price paid in all the cases where a sale does happen.
The checkThe optimal reserve sits above the seller's own value precisely so that some mutually beneficial trades fail. That loss is paid for by the higher prices in the cases where sale occurs.
Try itA seller values the item at nothing and faces one buyer whose value is spread evenly between zero and a hundred. Compute expected revenue with a reserve of fifty, then with no reserve. The reserve wins, and it wins by refusing to sell half the time.
Know these first
Easily confused with
Sources
- 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.