Reservation Values and Regret in Laboratory First-Price Auctions: Context and Bidding Behavior

[Author Affiliation]Theodore L Turocy, , , , T.Turocy@uea.ac.ukElizabeth Watson, , , , ewatson1@trinity.edu1. IntroductionIf you've never been surprised by the effect that a small change in instructions can have, then you've never tried it. Vernon Smith, keynote plenary session, World Meeting of the Economic Science Association, Rome, Italy, June 2007A long-standing puzzle in laboratory first-price private-values auctions is that subjects bid significantly more aggressively than predicted by the risk-neutral Nash equilibrium. The survey of Kagel (1995) outlines the history of this result. The financial consequences to subjects of this aggressive bidding are substantial relative to the scale of incentives. For instance, in Turocy, Watson, and Battalio (2007), subjects in first-price private-values auctions averaged earnings around $13.00 for participating in 60 auction periods; if a typical subject had unilaterally switched to the risk-neutral equilibrium strategy, she would have increased her earnings by $8.00.This stylized fact warrants the close attention it has received in the literature as a result of the broader roles of laboratory experiments in auctions. Auction experiments have been used to refine auction models and theories of bidding (Cox, Roberson, and Smith 1982) and have informed the design of auction mechanisms in the field (for example, Roth [2002]). In order to use the results of laboratory experiments to draw inferences about the determinants of bidding behavior in real-world auctions, we must be able to assume that subjects focus on the same strategic considerations that we believe agents in the field entertain. In the standard theory of bidding in first-price private-values auctions (Vickrey 1961; Milgrom and Weber 1982), the strategic consideration faced by a bidder is a price-probability tradeoff. A higher bid increases the probability of winning the auction but decreases the consumer surplus the bidder gains when she wins because she pays a higher price.Some recent experiments, including those of Engelbrecht-Wiggans and Katok (2007, 2008, 2009), Filiz-Ozbay and Ozbay (2007), and Ockenfels and Selten (2005), investigate the hypothesis that aggressive bidding in laboratory first-price auctions is motivated by a difference in how subjects anticipate or react to the outcomes of winning versus not winning an auction. This line of inquiry is based on the observation that the bid that is optimal ex ante will not in general be the optimal bid ex post , after the results of the auction are known. If the bidder wins an auction by submitting a bid that is strictly higher than any other bid, she may realize that she would have been able to win the auction had she submitted a lower bid and therefore could have increased her earnings; this is "winner regret." Conversely, if the bidder loses the auction, but the winning bid turns out to be less than her value, she could have bid higher and made positive earnings instead of zero earnings; this is "loser regret." Theoretical results in the literature on regret in auctions, dating to Engelbrecht-Wiggans' (1989) analysis of optimal bidding with regret, predict that higher bids result when loser regret is relatively more salient to subjects than winner regret.In this article, we examine how the exposition of the laboratory auction environment affects the strategic considerations faced by a bidder and might lead to the greater salience of loser regret implied by the results in the literature on regret in auctions. In most first-price auction experiments conducted to date, subjects are instructed that they have a privately known idiosyncratic "resale value" for the object being auctioned. The winning bidder purchases the object at the price she bid. She then sells it back to the experimenter for her resale value and earns the difference between her resale value and her bid. The other bidders do not purchase the object, have nothing to re-sell to the experimenter, and thus have earnings of zero. …