Polyhedral Clinching Auctions for Two-Sided Markets

In this paper, we present a new model and mechanisms for auctions in two-sided markets of buyers and sellers, where budget constraints are imposed on buyers. Our model incorporates polymatroidal environments and is applicable to a variety of models that include multiunit auctions, matching markets, and reservation exchange markets. Our mechanisms are built on the polymatroidal network flow model by Lawler and Martel. Additionally, they feature nice properties such as the incentive compatibility of buyers, individual rationality, Pareto optimality, and strong budget balance. The first mechanism is a two-sided generalization of the polyhedral clinching auction by Goel et al. for one-sided markets. The second mechanism is a reduce-to-recover algorithm that reduces the market to be one-sided, applies the polyhedral clinching auction by Goel et al., and lifts the resulting allocation to the original two-sided market via the polymatroidal network flow. Both mechanisms are implemented by polymatroid algorithms. We demonstrate how our framework is applied to the Internet display advertisement auctions.