Winner's curse

The winner's curse is a phenomenon that may occur in common value auctions with incomplete information. In short, the winner's curse says that in such an auction, the winner will tend to overpay. The winner may overpay or be "cursed" in one of two ways: 1) the winning bid exceeds the value of the auctioned asset such that the winner is worse off in absolute terms; or 2) the value of the asset is less than the bidder anticipated, so the bidder may still have a net gain but will be worse off than anticipated.^[1] However, an actual overpayment will generally occur only if the winner fails to account for the winner's curse when bidding (an outcome that, according to the revenue equivalence theorem, need never occur).

Explanation

In a common value auction, the auctioned item is of roughly equal value to all bidders, but the bidders don't know the item's market value when they bid. Each player independently estimates the value of the item before bidding.

The winner of an auction is the bidder who submits the highest bid. Since the auctioned item is worth roughly the same to all bidders, they are distinguished only by their respective estimates of the market value. The winner, then, is the bidder making the highest estimate. If we assume that the average bid is accurate, then the highest bidder overestimates the item's value. Thus, the auction's winner is likely to overpay.

More formally, this result is obtained using conditional expectation. We are interested in a bidder's expected value from the auction (the expected value of the item, minus the expected price) conditioned on the assumption that the bidder wins the auction. It turns out that for a bidder's true estimate the expected value is negative, meaning that on average the winning bidder is overpaying.

Savvy bidders will avoid the winner's curse by bid shading, or placing a bid that is below their ex ante estimation of the value of the item for sale—but equal to their ex post belief about the value of the item, given that they win the auction. The key point is that winning the auction is bad news about the value of the item for the winner. It means that he or she was the most optimistic and, if bidders are correct in their estimations on average, that too much was paid. Therefore savvy bidders revise their ex ante estimations downwards to take account of this effect.

The severity of the winner's curse increases with the number of bidders. This is because the more bidders, the more likely it is that some of them have overestimated the auctioned item's value. In technical terms, the winner's expected estimate is the value of the n^th order statistic, which increases as the number of bidders increases. In other words, more bidders = higher winner's curse.

There is often confusion that winner's curse applies to the winners of all auctions. However, it is worth repeating here that for auctions with private value (i.e. when the item is desired independent of its value in the market), winner's curse does not arise. Similarly there may be occasions when the average bid is too low relative to exterior market conditions e.g. a dealer recognising an antique or other collectable as highly saleable elsewhere when other bidders do not have the necessary expertise.

Examples

Since most auctions involve at least some amount of common value, and some degree of uncertainty about that common value, the winner's curse is an important phenomenon.

In the 1950s, when the term winner's curse was first coined, there was no accurate method to estimate the potential value of an offshore oil field. So if, for example, an oil field had an actual intrinsic value of $10 million, oil companies might guess its value to be anywhere from $5 million to $20 million. The company who wrongly estimated at $20 million and placed a bid at that level would win the auction, and later find that it was not worth as much.

Other auctions where the winner's curse is significant:

Spectrum auctions in which companies bid on licenses to use portions of the electromagnetic spectrum. Here, the uncertainty would come from, for example, estimating the value of the cell phone market in New York City.
IPOs, in which bidders need to estimate what the market value of a company's stock will be.
Pay per click advertising online, in which advertisers gain higher ranking if they bid higher amounts per click from a search engine user.

Related uses

Main article: Regression toward the mean

The term winner's curse is also used in statistics to refer to the regression toward the mean phenomenon, particularly in genome-wide association studies and epidemiology. In studies involving many tests on one sample of the full population, the consequent stringent standards for significance make it likely that the first person to report a significant test (the winner) will also report an effect size much larger than is likely to be seen in subsequent replication studies.^[2]

References

↑ Thaler, Richard H. (1988). "Anomalies: The Winner's Curse". Journal of Economic Perspectives. 2 (1): 191–202. doi:10.1257/jep.2.1.191. JSTOR 1942752.
↑ Ioannidis, John P. A. (2008). "Why most discovered true associations are inflated". Epidemiology. Lippincott Williams & Wilkins. 19 (5): 640–648. doi:10.1097/EDE.0b013e31818131e7. PMID 18633328.

External links

www.gametheory.net — applet demonstrating the winner's curse.
www.techcentralstation.com — article explaining the winner's curse in the context of the Google IPO.
The Winner's Curse in Baseball — article on how the winner's curse affects bidding for free agents.

Topics in game theory

Definitions	Normal-form game Extensive-form game Escalation of commitment Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian Nash equilibrium Perfect Bayesian equilibrium Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Gibbs equilibrium Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Screening game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game n-player game Large Poisson game Nontransitive game Global games Strictly determined game Potential game

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem Rendezvous problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Albert W. Tucker Amos Tversky Ariel Rubinstein Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin Jean Tirole Jean-François Mertens John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Thomas Schelling William Vickrey

See also	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons Tyranny of small decisions

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