Pricing Valid Cuts for Price-Match Equilibria

TL;DR

This paper introduces a novel method to generate anonymous linear prices in combinatorial auctions by using valid inequalities as artificial items, ensuring fairer pricing and proving the existence of these equilibria.

Contribution

It proposes the concept of price-match equilibrium (PME), a refined Walrasian equilibrium, and demonstrates its existence, properties, and computational methods in combinatorial auctions.

Findings

PME always exists for any combinatorial auction.

Artificial PME rules outperform other payment rules in experiments.

PME provides transparent and fair pricing in complex auction settings.

Abstract

We use valid inequalities (cuts) of the binary integer program for winner determination in a combinatorial auction (CA) as "artificial items" that can be interpreted intuitively and priced to generate Artificial Walrasian Equilibria. We thus provide a method for converting a CA problem that admits only non-anonymous, nonlinear bundle prices into one that admits anonymous linear prices over the augmented item space, forestalling ex-post bidder complaints about opaque and strongly discriminatory pricing. To this end, we introduce a refinement of the Walrasian equilibrium which we call a "price-match equilibrium" (PME) in which all prices are justified by providing an iso-revenue reallocation for the hypothetical removal of any single bidder. We prove the existence of PME for any CA and characterize their economic properties and computation. We implement minimally artificial PME rules and compare them with other prominent CA payment rules in the literature.