Valuation Uncertainty and Imperfect Introspection in Second-Price Auctions

David R.M. Thompson, Kevin Leyton-Brown

In auction theory, agents are typically presumed to have perfect knowledge of their valuations. In practice, though, they may face barriers to this knowledge due to transaction costs or bounded rationality. Modeling and analyzing such settings has been the focus of much recent work, though a canonical model of such domains has not yet emerged. We begin by proposing a taxonomy of auction models with valuation uncertainty and showing how it categorizes previous work. We then restrict ourselves to single-good sealed-bid auctions, in which agents have (uncertain) independent private values and can introspect about their own (but not others') valuations through possibly costly and imperfect queries. We investigate second-price auctions, performing equilibrium analysis for cases with both discrete and continuous valuation distributions. We identify cases where every equilibrium involves either randomized or asymmetric introspection. We contrast the revenue properties of different equilibria, discuss steps the seller can take to improve revenue, and identify a form of revenue equivalence across mechanisms.

Subjects: 7.1 Multi-Agent Systems; Please choose a second document classification

Submitted: Apr 25, 2007

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