Thursday, February 16, 2006

how to bid on blake's watercolors: auction theory


(Some of this is from an online auction theory primer.)

Auctions aren't just used to raffle off Blake watercolors: the govt sells t-bills, mineral rights, and the radio spectrum this way. So billions of dollars ride on auction theory every day.

The basic auction theory economic/game-theory model is a (1) fixed set of (2) symmetric (3) risk-neutral bidders with (4) independent information who bid (5) costlessly and (6) independently for (7) one object. Relaxing these assumptions is the main work of auction theory.

Consider the ascending-bid (English) and descending-bid (Dutch) auctions. It might seem clear that the Dutch auction will get thehouse a larger price. If bidders state their honest subjective values, this is true: an English auction will get the house the second-highest bidder's value (within an auction increment), while the Dutch auction receives the highest. Of course, if there are "many" bidders in some sense, then the results converge. Also, if the bidders behave strategically, rather than giving the independent bids in both types of auctions, there are circumstances in which a Dutch auction will bring a lower price than English. This can happen if bidders are very uncertain about the value of the good: the ascending auction can give signals, and encouragement, about the true value as bidders drop out. (Click on "Read..." to see more.)

Auctions depend strongly on asymmetric information. (If all bidders have equivalent information, most auction models are trivial.) There are two extreme models of information. The pure private-value model assumes that everyone has their own subjective value, and wouldn't care if they found someone else's value. The pure common-value model assumes the good has an objective market value which is only imperfectly known; each bidder has access to certain information, and finding out another's info might change your bid. The private-value model might be corrupted if you find out that others highly value the object: it might make you subjectively appreciate it more, or make you conscious of its possible resale value.

The winner's curse is a basic conundrum: auctions with simplifying behavioral models are usually shown to generate a sale price higher than the objective value of the good. If bidders take into account the bad news that others' signals generate (by dropping out), the winner's curse price and the objective value may converge. It's the auction house's job to hide some of this information, but without making the auction so uncertain that bidders (who are often risk-averse) low-ball the price.

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