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.

A Two-Sided Price-Decoupled Pay-As-Bid Auction Approach for the Clearing of Day-Ahead Electricity Markets

In this paper we propose a possible alternative for conventional pay-as-clear type multiunit auctions commonly used for the clearing of day-ahead power exchanges, and analyse some of its characteristic features in comparison with conventional clearing. In the proposed framework, instead of the concept of the uniform market clearing price, we introduce limit prices separately for supply and demand bids, and in addition to the power balance constraint, we formulate constraints for the income balance of the market. The total traded quantity is used as the objective function of the formulation. The concept is demonstrated on a simple example and is compared to the conventional approach in small-scale market simulations.

Efficient multiunit auctions for normal goods

I study multiunit auction design when bidders have private values, multiunit demands, and non‐quasilinear preferences. Without quasilinearity, the Vickrey auction loses its desired incentive and efficiency properties. I give conditions under which we can design a mechanism that retains the Vickrey auction's desirable incentive and efficiency properties: (1) individual rationality, (2) dominant strategy incentive compatibility, and (3) Pareto efficiency. I show that there is a mechanism that retains the desired properties of the Vickrey auction if there are two bidders who have single‐dimensional types. I also present an impossibility theorem that shows that there is no mechanism that satisfies Vickrey's desired properties and weak budget balance when bidders have multidimensional types.