A Note on
over- and underbidding in Vickrey auctions:
Do we need a new theory?
Stefan Seifert Stefan Strecker
University of Karlsruhe
Department of Economics and Business Engineering Information Management and Systems
Englerstr. 14 76131 Karlsruhe
Germany
seifert@wiwi.uni-karlsruhe.de stefan.strecker@iw.uni-karlsruhe.de
August 31, 2003
Introduction
Truthful revelation of valuations is a dominant strategy in second-price sealed-bid auctions with private-values (Vickrey 1961). However, bidding above the dominant strategy price has persistently been observed in laboratory experiments (Kagel and Levin 1993; Harstad 2000). Harstad (2000) finds that “substantial overbidding by nearly all subjects in second-price auctions persists.”
In a recent experimental study of a private-values procurement scenario (Strecker and Seifert 2003), we have analyzed a multi-attribute second-score reverse auction, an adaptation of the Vickrey auction to the multi-attribute case (Milgrom 2000).
In contrast to the earlier experimental research mentioned above, our experiment has involved (i) a reverse auction in which a single buyer (bid-taker, auctioneer) solicits bids from multiple suppliers (bidders) and (ii) three-dimensional bids that are evaluated by a (monetary) utility or scoring function modelling the buyer’s preferences with respect to the price and two non-price quality attributes. This auction design awards the contract to the supplier, who has bid the highest utility score. He produces and delivers the object with the qualities offered to the buyer, but is paid a price such that the utility score of the transaction equals the second- highest utility score (Vickrey principle).
Given the earlier experimental results, we expected (i) bidders to deviate from the dominant strategy and (ii) more subjects to overbid than to underbid. Note that overbidding refers to bids that are more attractive to the auctioneer than bids according to the dominant strategy, i. e. in the chosen procurement setting bidders understatetheir true production costs and turn in bids with pricesbelow these costs.
We were surprised, however, to observe, that more bidders overstate than un- derstate their costs. We define a bid to be in line with the dominant strategy, if the difference between the bid price and the bidder’s true costs is not larger than one currency unit in the experiment. Based on that definition, only 19 of a total of 235 bids asked for a price that is lower than the true costs (overbidding), but 67 bids asked for a price that is higher than the true costs (underbidding). Thus, bidders underbid significantly more often than they overbid.1
The relation of under- to overbidding is remarkable in that overbidding is ex- plained by the illusion of increasing the probability of winning at no or little cost (Kagel 1995), but underbidding seems hard to justify. Departing from the domi- nant strategy by submitting a bid price higher than the production costs lowers the likelihood of winning an auction, but keeps the possible gains unaffected. While the phenomenon of persistent overbidding in the Vickrey auction is interesting in itself, we consider it an even more interesting question why bidders tend to underbid in the reverse Vickrey auction.
1Ties-discarded sign test, p <0.001.
We currently investigate the reversal of over- to underbidding in a procurement context. It seems that in our experiment bidders put a markup on top of their production costs in order to “guarantee” a minimum profit in case they win the auction. How can this behavior be explained?
The remainder of this extended abstract discusses Harstad (2000)’s theory in the light of our experimental results and presents the topic of the discussion, we would like to commence at the WISE 2003. Note that this is work in progress.
Feedback and Harstad’s theory
Harstad (2000) analyzes bidding behavior in the Vickrey auction in asales context and searches for explanations of overbidding. He considers models of bounded ratio- nality, but rejects them for several reasons: First, overbidding cannot be explained by “boundedly rational beliefs about rival’s behavior” (p. 274). Second, overbidding does not diminish with feedback but is persistent and even increases with greater experience, and third, experience in market institutions other than the Vickrey auc- tion significantly reduces overbidding. Instead, Harstad explains overbidding by the particular feedback mechanism that is symptomatic for the Vickrey auction: “in a second-price auction, a subject might overbid, win, and still make money” (p. 262).
The bidder might (mistakenly) consider such an experience as positive feedback.
Our new findings challenge the general validity of Harstad’s argument. According to his argument, a bidder in a procurement auction would offer to deliver the good at a price that is lower than his production costs (overbidding). If the difference between the production costs and the price is not too large, such a bidding strategy is sustainable in the sense that it generates positive bidder profits on average. In this case, the auction provides positive feedback to the winning bidder. On the other hand, the winning bidder might fear to lose business when bidding more defensively.
Consider now the feedback to a bidder who underbids in our experiment. If he wins the auction he learns that he could have offered a lower price without changing the outcome. Had he asked for a higher price, however, he might have risked to lose the auction. A bidder, on the other hand, who is not awarded the contract learns that apparently his price was too high and that a lower price would have increased his chances of winning the auction. He also knows that in the case of winning the auction he receives a non-negative surcharge in addition to the price he bid.
Thus, the peculiarity of feedback in the Vickrey auction is inadequate to explain underbidding in our experiment.
Framing effects
It has been known since Tversky and Kahneman (1981), that a decision-maker’s subjective conception of the acts, outcomes and contingencies associated with a
particular choice (decision frame) is controlled partly by the formulation of the problem. The framing effect pertains to a change of preferences between options as a function of the variation of frames.
One possible explanation for the observed prevalence of underbidding in our experiment is its framing as a reverse auction in a procurement scenario. However, this question has, to our knowledge, not been investigated so far. We hypothesize that the different auction context, a sales auction on the one hand and a procurement auction on the other hand, is one reason for the different strategies that bidders apply in a Vickrey auction.
Research hypothesis
The framing of a Vickrey auction as either a procurement or a sales auction affects deviations from the dominant strategy. Bidders tend to overbid (bid aggressively) in a sales context and tend to underbid (bid defensively) in a procurement context.
In order to test our hypothesis, we propose to conduct a further laboratory experiment that isolates the issue of framing (sales vs. procurement setting) and focuses on only one-dimensional bids. Consider for example the following three treatments of private-values auctions:2
A.Five biddersi= 1, . . . ,5 participate in asalesauction. Letv = (6,7,8,9,10) denote the valuations of the bidders for the auctioned object and v0 = 0 the val- uation of the seller. The equilibrium in dominant strategies is given by b∗A = v = (6,7,8,9,10). If all bidders stick to their dominant strategy, bidder 5 will win the auction and pay a price p∗A= 9.
B. Five bidders i = 1, . . . ,5 participate as suppliers in a procurement auc- tion. The buyer’s scoring function with respect to the delivery price is given by u0(p) = 20−p and the bidders’ (suppliers) costs of delivering the object by c = (14,13,12,11,10). The auction’s rules require the suppliers to bid a utility score u0 for the buyer. The supplier who bids the the highest utility score delivers the object and is payed a price such that the actual buyer’s utility equals the sec- ond highest bid. As above, the vector b∗B = b∗A = (6,7,8,9,10) of bids constitutes equilibrium in dominant strategies. The transaction price in equilibrium isp∗B = 11.
C. Again, five bidders i = 1, . . . ,5 participate as suppliers in a procurement auction. However, suppliers do not bid on utility scores but on prices. The supplier offering the lowest price wins the auction and is payed the second lowest bid. Note that the function t(b) = 20−b transforms strategies of treatment B to C (and vice
2Concise numbers are used for illustrative purposes and to simplify the argument. They are arbitrarily chosen and not intended for actual experimental investigations.
versa) without changing the outcome of the auction. Dominant strategies in C are given by b∗C =c= (14,13,12,11,10).
In all treatments A to C the equilibrium payoffs of the bidders are given by u∗A=u∗B =u∗C = (0,0,0,0,1), the auctioneer makes a profitu0 = 9 and the auction will generate a social gain of 10.
Our research hypothesis suggests that in an auction experiment according to treatment A bidders tend to overbid. As a result, bidder surplus will be lower and the auctioneer’s profit will be higher than in equilibrium. It also suggests that the opposite holds for treatment C.
If our research hypothesis holds true, Harstad’s theory based on the Vickrey auctions’s feedback mechanism should be revised. In this case treatment B might help to understand the difference. A new theory explaining bidding behavior in the Vickrey auction may focus on the context of the auction (sale vs. procurement) or the bidding language (treatment B vs. treatment C).
References
Harstad, R. M. (2000): “Dominant Strategy Adoption and Bidders’ Experience with Pricing Rules,” Experimental Economics, 3, 261–280.
Kagel, J. and D. Levin (1993): “Independent Private Value Auctions: Bidder Behavior in First, Second and Third Price Auctions with Varying Numbers of Bidders,” Economic Journal.
Kagel, J. H. (1995): “Auctions: A Survey of Experimental Research,” in The Handbook of Experimental Economics, ed. by J. H. Kagel and A. E. Roth, Prince- ton, NJ: Princeton University Press, 501–585.
Milgrom, P. (2000): “An Economist’s View on the B-to-B Marketplace—An Ex- ecutive White Paper,” Perfect Commerce Inc., www.perfect.com.
Strecker, S. and S. Seifert(2003): “Electronic Sourcing with Multi-Attribute Auctions,” Tech. rep., University of Karlsruhe, Information Management and Systems, submitted for review to the 37th Hawaii International Conference on System Sciences (HICSS-37), January 5–8, 2004.
Tversky, A. and D. Kahneman (1981): “The Framing of Decisions and the Psychology of Choice,” Science, 211, 453–458.
Vickrey, W.(1961): “Counterspeculation, Auctions, and Competitive Sealed Ten- ders,” Journal of Finance, 3, 8–37.
