Generalizing Deferred Acceptance Auctions to Allow Multiple Relinquishment Options

Abstract

Introduction and the Statement of the Problem. Reallocation of spectrum from current licensees TV broadcasters to mobile uses to promote e cient use of spectrum has become a public policy agenda. The Congress authorized the FCC to conduct incentive auctions for reallocations of spectrum in the UHF band. In this paper, we focus on the design of reverse auctions where TV stations submit bids to voluntarily relinquish spectrum rights to FCC in exchange for payments. The state of the art of the design of reverse auctions is the framework given in Paul Milgrom, Lawrence Ausubel, Jon Levin, and Ilya Segal (2012) and deferred acceptance auctions proposed by Paul Milgrom and Ilya Segal (2014). In deferred acceptance auctions, each seller submits a single o er. At each round, an o er is evaluated with its scoring function. The buyer deletes the o er with the highest score. Then the set of frozen sellers (i.e., the set of sellers who will be assigned back to the band because the scores are too high) will be updated and o ers are re-evaluated. Auctions end when only o ers with the zero score remain. The payment rule is determined by the threshold price that is the maximum amount that the seller can o er to sell. When bidders are single-minded (that is, a bidder can make only one bid), then, the deferred acceptance auctions are strategy-proof, can be implemented in descending clock auctions, nearlyoptimal, group strategy-proofness, and equivalent to payas-bid auctions. But the Spectrum Act 6403(a)(2) stipulates that bidders shall have multiple relinquishment options such as going o the air, moving to the VHF band, and channel sharing. When the seller can make only one o er, the seller has to choose which auction to bid. Then the payment depends on the choice of auctions by other bidders. Therefore, the seller’s choice of auctions can depend on other sellers’ choices. Thus sincere bidding may not be an equilibrium.