Students / Subjects

# Winner's Curse in First-Price Auctions

## Experimental Design

The following procedure is employed in most common value auction experiments. In each auction period, a common value V is chosen from a uniform distribution on [a, b]. Then each bidder is given a private signal S, which is drawn from a uniform distribution on [V-e, V+e]. e is common information. In first-price auctions, the bidder who bids the highest bid b wins the item and earns V-b. Other bidders earn zero profits.

Before bidders play for cash, several trial auction periods are provided. Each bidder is endowed with a fixed amount positive cash balance. If a bidder exhausts his budget during the experiment, he is declared bankrupt and no longer allowed to bid.

Obviously, under this design bidders never lose money by bidding max{a, S-e}. According to the Bayesian-NashEquilibrium thoeretical prediction, bidders bid slightly higher than S-e (given that S-e is greater than a) in equilibrium.

## Experimental Results

The experimental results show that the winner's curse is a pervasive problem for inexperienced bidders--there are numerous bankrupcies and on average bidders earn zero or negative profits. The winner's curse for inexperienced bidders has been reported under a variety of treatment conditions and for different subject populations. (Kagel et al. 1989, Lind and Plott 1991, and Dyer et al 1989.)

Kagel and Levin (1986) report auctions for moderately experienced bidders, who had at least participated in one prior first-price common value auction experiment. They find that for small groups (auctions with 3 or 4 bidders) the winner's curse goes away and on average experienced bidders earn positive profits. However, for large groups (auctions with 6 or 7 bidders) although profits earned by experienced bidders are substancially higher than profits earned by inexperienced bidders, the winner's curse still persists.

## Explanations for the Experimental Results

Despite the nature of the winner's curse, there might be two experimental design problems which cause aggressive bidding behavior.

In the Kagel and Levin (1986) design, subjects never lose more than their starting cash balance. The aggressive bidding behavior might come from this "limited liability" feature. In response to the limited liability issue, Lind and Plott (1991) design their experiment without limited liability, and find that the winner's curse still persists. Therefore, the "limited liability" might not be the reason for the overly aggressive bidding reported.

Another possible explanation for the winner's curse could be the lack of an alternative to bidding for bidders making losses from overbidding. Cox, et al. (2001) extend bidding theory and experimental design to include a salient characteristic of naturally-occurring auctions: (a) entry into an auction is endogenous and has an opportunity cost of foregone earnings from alternative activities; and (b) auction market competition determines the number of active bidders as well as their bidding strategies. They find that the winner's curse is not a serious problem in markets with 3-8 experienced bidders but that it continues to be significant in markets with 12 experienced potential bidders.

## References

• Cox, J. C., S. Dinken, and J. T. Swarthout, 2001. "Endogenous entry and exit in common value auctions." Experimental Economics, 4: 163-181.
• Dyer, D., J. H. Kagel and D. Levin. 1989. A comparison of naive and experienced bidders in common value offer auctions: A laboratory analysis. Economic Journal, 99:108-15. \
• Kagel, J. H., and D. Levin. 1986. The winner's curse and public information in common value auctions. American Economic Review, 76:894-920.
• Kagel, J. H., D. Levin, R. Battalio, and D. J. Meyer. 1989. First-price common value auctions: Bidder behavior and the winner's curse. Economic Inquiry, 27:241-58.
• Lind, B., and C. R. Plott. 1991. The winners curse: Experiments with buyers and with sellers. American Economic Review. 81: 335-46.