INDIVIDUAL BEHAVIOR AND BIDDING HETEROGENEITY IN SEALED BID AUCTIONS WHERE THE NUMBER OF BIDDERS IS UNKNOWN

I. INTRODUCTION Most of the work in sealed bid auction theory and related experimental work has focused on the case in which the number of bidders is known. This is, of course, not always the case in naturally occurring environments. For instance, construction firms submitting bids in a sealed bid procurement auction may not know exactly how many other firms have completed the costly process of preparing and submitting a bid until bidding has closed. There is a body of theory to address environments with an unknown number of bidders (McAfee and McMillan 1987; Matthews 1987; Harstad, Kagel, and Levin 1990; Krishna 2002). (1) The purpose of this article is to provide theoretical considerations and analysis of a large data set of individual bids from laboratory sealed bid auction markets in which buyers have some information about the number of rivals, but not certainty. (2) According to the received theory, the availability of information about the number of rivals, as expected, directly affects bidding and therefore seller revenue in first-price (FP) auctions but should not affect bidding in the second-price (SP) auctions. Although bidding own valuation is optimal in SP auctions (regardless of the number of bidders), the majority of previous experimental work on auctions with known number of bidders has shown systematic deviation (Kagel 1995) while a few studies report coincidence with theory (see Isaac and James 2000b for an extended discussion). Earlier work on FP auctions with known number of bidders indicated systematic overbidding compared to risk neutral equilibrium. Risk aversion has been suggested as one of the possible explanations for observed overbidding (Cox, Roberson, and Smith 1982). Dyer, Kagel, and Levin (1989) is the only previous experimental study looking at individual bidding in auctions where the number of bidders is unknown and their design is different from this study. They look at FP auctions with restricted auction size of either six or three participants and ask subjects to submit three bids (two bids for contingent bidding procedure and one bid for noncontingent bidding procedure). Subjects submit all three bids simultaneously and do not know at the time which procedure will be used. They find overbidding in this environment compared to risk neutral Nash equilibrium. Although we test for deviation from risk neutral bidding strategy in a more general setting, our study also addresses a broader set of questions. Previous studies of open-bid ascending "silent" auctions suggested that there may have been revenue loss to the sellers by bidders "guarding" their higher valued items, that is, remaining physically proximate to the bidding stations (Isaac and Schnier 2005). The possibility that "guarding" was at the root of the revenue reductions was investigated by Isaac and Schnier (2006), who replaced the open-bid ascending silent auctions with both FP and SP sealed bid auctions, which is the environment studied in this article. Their paper reported on the aggregate revenue effects of the switch to sealed bid auctions but did not look at individual behavior. It is clear that such analysis of individual bidding behavior must be informed by theories of bidding with an unknown number of rivals, because such is the reality facing bidders in a multiple sealed bid silent auction context. In addition, data from a noncomputerized experiment closely approximating field auctions allows the analysis of possible behavioral adjustments in the field, for example, the attempt to "guard" the item and count the number of bidders. Such an analysis is presented in this article. (3) Our analysis of FP auctions contributes to the discussion about the causes of heterogeneous deviation of individual bidding from risk neutral theory. Cox, Roberson, and Smith (1982) and Cox, Smith, and Walker (1988) reported heterogeneous bidding above risk neutral equilibrium in FP auctions for mechanisms with fixed number of bidders and Palfrey and Pevnitskaya (2008) for auctions with endogenous entry, where the number of bidders was known at the time of submitting a bid. …