Multiple-Object, Discriminatory Auctions with Bidding Constraints: A Game-Theoretic Analysis

This paper examines the existence and characterization of pure strategy Nash equilibria in multiple-object auction games in which buyers face a binding constraint on exposure. There are five major results. First, symmetric Nash equilibria exist if and only if there are two or less buyers and two or less items. Second, a Nash equilibrium may not exist if the seller sets a positive reservation bid. Third, asymmetric solutions to symmetrically parameterized games typically involve “high-low” strategies: each buyer submits positive bids only on some restricted subset of the items. Fourth, Nash equilibria typically generate zero “surplus” to the buyers. Fifth, when asymmetric solutions exist and the buyers are identical, these solutions are never unique.