An Efficient Auction for Non Concave Valuations

We study an implementation problem for settings where some of the participants have non concave valuations. These valuations are common in the wireless industry in cases where primary users with property rights on a spectrum band would like to lease some of it to low power users. The non concavity void the efficiency results for standard designs of dynamic auctions. Moreover, policy concerns in such settings is often to prevent collusion and fraudulent bidding, therefore static Vickrey mechanisms do not provide the right incentives. We present an alternative mechanism that selects a core outcome that minimizes seller revenue. Such an allocation is efficient in equilibrium, limits the incentives to use shills, maximizes incentives for truthful bidding, and gives a Vickrey outcome whenever the latter is in the core.