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Generalized Deferred Acceptance Auctions with Multiple Relinquishment Options for Spectrum Reallocation

This paper studies the design of reverse auctions in the US incentive auctions where TV broadcasters in the UHF band offer to relinquish the usage right or to relocate to another band to increase the spectrum for mobile communication uses. The state of the art is the deferredacceptance auctions by Paul Milgrom and Ilya Segal (2014) that determine allocations based on scores and are strategy-proof when sellers are single-minded. But when sellers have multiple relinquishment options and are restricted to be single-minded, there would be possibilities of strategic considerations about which option the seller should bid. Nevertheless just allowing multiple bids is not possible since a seller switching one option to another may violate interference constraints. To resolve this issue, this paper proposes generalized deferred acceptance auctions with the supplementary phase where sellers make multiple offers, the buyer does not need to recalculate interference constraints, and are strategy-proof. This auction can be regarded as a generalization of ‘ladder auctions’ of Jon Levin, Paul Milgrom, and Ilya Segal (2012) for multiple offers. These results show generalities and robustness of incentive auctions design described in FCC NPRM 12-118, Paul Milgrom, Larry Ausubel, Jon Levin, and Ilya Segal (2012), and Paul Milgrom and Ilya Segal (2014).