# Common value auction

In common value auctions the value of the item for sale is identical amongst bidders, but bidders have different information about the item's value. Examples include Treasury bill auctions, initial public offerings, and spectrum auctions. This stands in contrast to a private value auction where each bidder's private valuation of the item is different and independent of peers' valuations.[1] Between these two extremes are interdependent value auctions, where bidder's valuations (e.g., ${\displaystyle \theta _{i}=\theta +\nu _{i}}$) can have a common value component (${\displaystyle \theta }$) and a private value (${\displaystyle \nu _{i}}$) component. The two components can be correlated so that one bidder's private valuation can influence another bidder's valuation.[2] These types of auctions comprise most real-world auctions and are sometimes confusingly referred to as common value auctions also.

One important phenomenon occurring in common value auctions is the winner's curse. Bidders have only estimates of the value of the good. If, on average, bidders are estimating correctly, the highest bid will tend to have been placed by someone who overestimated the good's value. This is an example of adverse selection, similar to the classic "lemons" example of Akerlof. Rational bidders will anticipate the adverse selection, so that even though their information will still turn out to have been overly optimistic when they win, they do not pay too much on average.

Sometimes the term winner's curse is used differently, to refer to cases in which naive bidders ignore the adverse selection and bid sufficiently more than a fully rational bidder would that they actually pay more than the good is worth. This usage is prevalent in the experimental economics literature, in contrast with the theoretical and empirical literatures on auctions.

In a classic example of a pure common values auction used to illustrate the winner's curse, a jar full of quarters is auctioned off. The jar will be worth the same amount to anyone. However, each bidder has a different guess about how many quarters are in the jar. On average, these guesses might be correct, but if the winner is the bidder with the most optimistic guess, his guess will typically be too high.

Examples of winner's curse may occur in auctions in bidding for very prized paintings, art pieces, antiques etc.

## Relationship to Bertrand competition

Common-value auctions are comparable to Bertrand competition. Here, the firms are the bidders and the consumer is the auctioneer. Firms "bid" prices up to but not exceeding the true value of the item. Competition among firms should drive out profit. The number of firms will influence the success or otherwise of the auction process in driving price towards true value. If the number of firms is small, collusion may be possible. See Monopoly, Oligopoly.

## References

1. ^ Susan Athey and Ilya Segal (2013). "An Efficient Dynamic Mechanism" (PDF). Econometrica 81 (6): 2463–2485. doi:10.3982/ECTA6995.
2. ^ Dirk Bergemann and Stephen Morris (2013). "Robust Predictions in Games with Incomplete Information" (PDF). Econometrica 81 (4): 1251–1308.