We find new equilibria of minimum-revenue core-selecting (MRCS) auctions that, in contrast to previously identified equilibria, involve overbidding - bidding more than one's true value for some packages of goods. With full information, every MRCS auction in every possible setting has equilibria with overbidding and these equilibria have different properties than the previously known equilibria with bid shading. Namely, they can lead to strictly higher revenues for the seller and larger price differences among bidders. Previous studies of MRCS games with incomplete information assumed restricted strategy spaces that prevented overbidding. In this paper, we allow bidders access to their complete strategy sets and show that, in some settings, overbidding occurs in all Bayesian equilibria in undominated strategies. In a simple setting with independent private values, equilibrium strategies of a particular set of MRCS auctions employ a mixture of bid shading and overbidding. These new equilibria improve expected effi ciency relative to equilibria with restricted strategy spaces and lead to higher expected revenues than those from the Vickrey package auction. A second incomplete-information setting demonstrates that equilibria with overbidding can be in some sense unique. In this setting, every Bayesian equilibrium in undominated strategies of every MRCS auction has at least one bidder who overbids and there is no bid shading on winning packages. Overbidding eliminates the threshold problem, leading to an effi cient assignment and payoffs that are in the core with respect to the true values.
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