Multi-option descending clock auction

A descending clock auction (DCA) is a mechanism for buying items from multiple sellers. The auctioneer starts by offering bidders high prices and gradually decreases the prices while there is competition. The literature has focused on the vanilla case where each bidder has two options: to accept or reject the offered price. However, in many settings—such as the FCC’s imminent incentive auction—each bidder may be able to sell one from a set of options. We present a multi-option DCA (MDCA) framework where at each round, the auctioneer offers each bidder different prices for different options, and a bidder may find multiple options still acceptable. A key component is the technique for deciding how to set prices during the MDCA. This is significantly more difficult in an MDCA than in a DCA. We develop a Markov chain model for representing the dynamics of each bidder’s state (which options are still acceptable), as well as an optimization model and technique for finding prices to offer to the different bidders for the different options in each round—using the Markov chain. The optimization minimizes total payment while ensuring feasibility in a stochastic sense. We also introduce percentile-based approaches to decrementing prices. Experiments with real FCC incentive auction interference constraint data reveal that the optimization-based approach dramatically outperforms the simple percentile-based approach both under symmetric and asymmetric bidder valuation distributions—because it takes feasibility into account in pricing. Both techniques scale to the large.