On Revenue-Optimal Dynamic Auctions for Bidders with Interdependent Values

Abstract

In a dynamic market, being able to update one's value based on information available to other bidders currently in the market can be critical to having profitable transactions. This is the model of interdependent values (IDV): a bidder's value can explicitly depend on the private information of other bidders. In this paper we present preliminary results about the revenue properties of dynamic auctions for IDV bidders. We adopt a computational approach to design single-item revenue-optimal dynamic auctions with known arrivals and departures but (private) signals that arrive online. In leveraging a characterization of truthful auctions, we present a mixed-integer programming formulation of the design problem. Although a discretization is imposed on bidder signals the solution is a mechanism applicable to continuous signals. The formulation size grows exponentially in the dependence of bidders' values on other bidders' signals. We highlight general properties of revenue-optimal dynamic auctions in a simple parameterized example and study the sensitivity of prices and revenue to model parameters.