Pricing Valid Cuts for Price-Match Equilibria
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.
Cite
@article{arxiv.2502.15893,
title = {Pricing Valid Cuts for Price-Match Equilibria},
author = {Robert Day and Benjamin Lubin},
journal= {arXiv preprint arXiv:2502.15893},
year = {2026}
}