Bidding in multi-unit auctions under limited information

Abstract

Multi-unit auctions frequently take place in environments with limited information, such as in new markets and under volatile macroeconomic conditions. We characterize optimal prior-free bids in such auctions; these bids minimize the maximal loss in expected utility resulting from uncertainty surrounding opponent behavior. We show that optimal bids are readily computable in this environment despite bidders having multi-dimensional private information. In the pay-as-bid auction the prior-free bid is unique; in the uniform-price auction the prior-free bid is unique if the bidder is allowed to determine the quantities for which they bid, as in many practical applications. We compare prior-free bids and auction outcomes across auction formats; while outcome comparisons are ambiguous, pay-as-bid auctions tend to generate greater revenue and welfare than uniform-price auctions when bidders' values are dispersed. We also compare outcomes in limited-information environments to outcomes in high-information environments, modeled as bidders playing Bayes-Nash equilibrium, and show that Bayes-Nash outcomes dominate prior-free outcomes when the auction is competitive.