Coordination and pricing in multi-object auctions

Much research has focused on the design of efficient combinatorial auctions. Recent gametheoretical work highlights that strategy-proof ascending mechanisms for general valuations are impossible due to inherent free-rider problems in specific situations. We argue that these negative results are due to assumptions in Bayesian games which typically do not hold in online combinatorial auctions. However, bidders in larger ascending combinatorial auctions face a substantial coordination problem, which has received little attention in the literature. Losing bidders need to submit non-overlapping package bids which are high enough to outbid the standing winners. The proposed auction leverages the information that the auctioneer collects throughout the auction about the preferences of individual bidders and suggests prices for the members of losing bidder coalitions, which in total would make a given coalition winning. We model the bidder's bundle selection problem as a coordination game, which provides a theoretical rationale for bidders to agree to these prices even though they might not maximize payoff in this round. Results of experiments with human participants demonstrated that this type of pricing substantially reduces the number of auction rounds and bids necessary to find a competitive equilibrium and even leads to higher efficiency. This rapid convergence is crucial for the practical viability of combinatorial auctions in larger markets.