Most of the rational explanations for the winner’s curse deal with identifying imper- fections in thefield data used to demonstrate the effect. Unfortunately, it is not generally possible to observe individual information about the value of an object in afield setting. As well, it is impossible to determine the expected profit for an object or endeavor with any degree of accuracy.
For example, in studying the oil lease contracts, it is necessary to assume specific discount factors for future consumption in order to determine if the net present value of returns is negative or positive. Assuming less discounting for the future provides a larger return. Further, there were tremendous increases in the price of oil over the period generally studied that are unlikely to have been anticipated. Similarly, estimating the overpayment of baseball players relies heavily on the underlying assumptions of that player’s value. Certainly there may be factors other than slugging, strikeouts, and walks. Finally, risk aversion alters the optimal bid and generally leads to higher bids. Thus, if winning bidders are risk averse, we would expect them to display profits that are below the expected payout- maximizing amount on average, though these profits should not be negative on average. All of these factors make it difficult to say with certainty that the winner’s curse has been observed in the wild. Thus, many have suggested that the winner’s curse is simply an illusion. However, this phenomenon appears to have had tremendous impacts on the way several industries respond to unknown values. The simple presence of mechanisms such as those found in the construction industry is tangible evidence that people develop heuristics to deal with the problem of the winner’s curse, while not fully understanding the mathematics behind the problem itself. These heuristics develop out of systematic experience, providing a key point of evidence that the curse exists in some contexts and is strong enough to lead to long-term changes in institutions.
Biographical Note
© KENDRA LUCK/San Fran cisco Chroni cle/CorbisMatthew Rabin (1963–)
B.A., University of Wisconsin at Madison, 1984; Ph.D., Massachusetts Institute of Technology, 1989; held faculty positions at the University of California at Berkeley
Matthew Rabin conducted his undergraduate study in economics and mathematics. His training has led to an approach that is behavioral, yet based on rigorous mathematical modeling of the underlying phenomena. Much of this work employs behavioral concepts in a game-theory setting. His earliest work posits that people consider the motivations of others when deciding how to behave. For example, one might wish to help someone who has been nice to one in the past
T H O U G H T Q U E S T I O N S
1. Consider that you are preparing to sell some antique items at auction. How might you design the auction so as to receive the highest possible sale price? What sorts of behavioral anomalies will be important to consider? What role will the number and experience of the bid- ders play in the auction?
2. Consider now that you are preparing to purchase an item at auction for your personal use. What factors should you consider in forming your bid? What behavioral tendencies should you try to avoid? What if you were purchasing the item for resale at a later date instead?
3. Building contractors bidding on a building project
often calculate their anticipated costs, add some per- centage for profit, and then double this number and submit it as a bid. Similar rules of thumb have been reported in other auction arenas. Why do you think such rules of thumb developed? What purpose do they serve? In what ways might the contractors be worse off for using this rule of thumb?
4. Suppose that two people are engaged in a Vickrey
auction for a good with two possible values: $10 or $20. Further, suppose each bidder receives a signal of the value, xn, where xnis equal to the true value with
probability 0.8, and equal to the other possible value with probability 0.2. No information other than this signal is available. Each player must select a bid based on his own signal. What bidding strategy would be
suggested by the fully cursed equilibrium (e.g., what should you bid if you receive a signal of $10 and what should you bid if you receive a signal of $20)? Sup- pose that players can only bid integer amounts, and follow the example given in the text. Thus, if player 1 draws x1= 10, the mean value of winning the auction
is μ = 0.8 × 10 + 0.2 × 20 = 12, the probability of signals that player 2 might receive is (similar to equation 5.14)
p x2 =
0.8× 0.8 + 0.2 × 0.2 = 0.68 if x2= 10
0.8× 0.2 + 0.2 × 0.8 = 0.32 if x2= 20.
If player 1 draws x1= 20, the expected value of win-
ning the auction isμ = 0.8 × 20 + 0.2 × 10 = 18, and the probability distribution of signals that player 2 might receive is
p x2 =
0.8× 0.8 + 0.2 × 0.2 = 0.68 if x2= 20
0.8× 0.2 + 0.2 × 0.8 = 0.32 if x2= 10
Suppose that in the event of a tie, both players receive the value of the object. First try the strategy in which each player bids the expected value of the gamble given the signal each has received. Show that this constitutes a cursed equilibrium. What is the expected profit in this case (the actual, not perceived)? Do these strategies constitute a Bayesian Nash equilibrium? If not, can youfind the Bayesian Nash equilibrium? and might wish to harm those who have harmed one in the past. His works have contributed to behavioral theory of auctions, risk and uncertainty, the impacts of cheap talk (nonbinding talks) in games, the discounting and anticipation of future events, probability judgment bias, and welfare analysis. His colleagues describe him as a voracious reader, approaching new research byfirst pulling all related literature from any discipline that may be connected to it. In 2001, he won the John Bates Clark Medal, which is generally awarded to the economist younger than 40 years who has contributed the most to thefield. He has won the MacArthur fellowship (often called the“Genius” fellowship). Personally, Matthew Rabin is known as an engaging teacher and presenter, endowed with more than his fair share of humor. As an example of the humor inherent in his personality, his personal résumé lists hisfirst professional honor as being voted “Most Likely to Express His Opinion,” by the Springbrook High School class of 1981.
R E F E R E N C E S
Ariely, D., A. Ockenfels, and A.E. Roth.“An Experimental Analysis of Ending Rules in Internet Auctions.” RAND Journal of Eco- nomics 36(2005): 890–907.
Baraji, P., and A. Hortaçsu.“The Winner’s Curse, Reserve Prices and Endogenous Entry: Empirical Insights from eBay Auctions.” RAND Journal of Economics 34(2003): 329–355.
Capen, E.C., R.V. Clapp, and W.M. Campbell.“Competitive Bidding in High-Risk Situations.” Journal of Petroleum Technology 23(1971): 641–653.
Cassing, J., and R.W. Douglas.“Implications of the Auction Mech- anism in Baseball’s Free Agent Draft.” Southern Economic Journal 47(1980): 110–121.
Cox, J.C., B. Roberson, and V.L. Smith.“Theory and Behavior of Single Object Auctions.” Research in Experimental Economics 2(1982): 1–43.
Dyer, D., and J.H. Kagel.“Bidding in Common Value Auctions: How the Commercial Construction Industry Corrects for the Winner’s Curse.” Management Science 42(1996): 1437–1475.
Eyster, E., and M. Rabin. “Cursed Equilibrium.” Econometrica 73(2005): 1623–1672.
Kagel, J.H., R.M. Harstad, and D. Levin.“Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study.” Econometrica 55(1987): 1275–1304. Kagel, J.H., and D. Levin.“The Winner’s Curse and Public Infor-
mation in Common Value Auctions.” American Economic Review 76(1986): 894–920.
Kagel, J.H., and J.-F. Richard.“Super-Experienced Bidders in First- Price Common Value Auctions: Rules of Thumb, Nash Equilib- rium Bidding, and the Winner’s Curse.” Review of Economics and Statistics 83(2001): 408–419.
Lucking-Reiley, D.“Using Field Experiments to Test Equivalence between Auction Formats: Magic on the Internet.” American Economic Review 89(1999): 1063–1080.
Mead, W.J., A. Moseidjord, and P.E. Sorensen.“The Rate of Return Earned by Lessees under Cash Bonus Bidding of OCS Oil and Gas Leases.” Energy Journal 4(1983): 37–52.
Roth, A.E., and A. Ockenfels.“Last-Minute Bidding and the Rules for Ending Second Price Auctions: Evidence from eBay and Amazon Auctions on the Internet.” American Economic Review 92(2002): 1093–1103.
Samuelson, W.F., and M.H. Bazerman. “The Winner’s Curse in Bilateral Negotiations.” Research in Experimental Economics 3(1985): 105–137.
Stahl, D.O., and P.W. Wilson.“On Players’ Models of Other Players: Theory and Experimental Evidence.” Games and Economic Behavior 10(1995): 218–254.
Wilson, R.“A Bidding Model of Perfect Competition.” Review of Economic Studies 44(1977): 511–518.