VCG-equivalent in expectation mechanism: General framework for constructing iterative combinatorial auction mechanisms

In this paper, we develop a new class of iterative mechanisms called a VCG-equivalent in expectation mechanism. Iterative auctions are preferred over their sealed-bid counterparts in practical settings, since they can avoid full revelation of type information. However, to guarantee that sincere strategies are an ex post equilibrium, the mechanism needs to achieve exactly the same outcome as the Vickrey-Clarke-Groves (VCG) mechanism. To guarantee that a mechanism is VCG-equivalent, it inevitably asks an irrelevant query, in which a participant has no incentive to answer the query sincerely. Such an irrelevant query causes unnecessary leakage of private information and a different incentive issue. In a VCG-equivalent in expectation mechanism, the mechanism achieves the same allocation as VCG, but the transfers are the same as VCG only in expectation. We show that in a VCG-equivalent in expectation mechanism, sincere strategies constitute a sequential equilibrium. Also, we develop a general procedure for constructing a VCG-equivalent in expectation mechanism that does not ask any irrelevant query. To demonstrate the applicability of this idea in a practical application, we develop a VCG-equivalent in expectation mechanism that can be applied to the Japanese 4G spectrum auction.