Efficient and Dominance Solvable Auctions with Interdependent Valuations

In auction environments in which agents have private values, the Vickrey auction induces agents to truthfully reveal their preferences and selects the efficient allocation accordingly. When the agents' valuations are interdependent, various generalizations of the Vickrey auction have been found which provide incentives for truthful revelation of all private information and preserve efficiency. However, these mechanisms generally do not provide the bidders with dominant strategies. The existing literature has therefore used a stronger equilibrium solution concept. In this paper we show that while the generalized VCG mechanism admits a multiplicity of equilibria, many of which are inefficient. We give conditions under which the efficiency equilibrium is the unique outcome of iterative elimination of ex post weakly dominated strategies. With two bidders, the standard single-crossing condition is sufficient. With more than two bidders, we show by example that a strengthening of the single-crossing condition is necessary.