Discrete Pricing in Multiobject Auctions with Unit Demand and Wealth Effects

We study an auction model for selling multiple heterogeneous objects, in which (i) each agent gets at most one object and has utility functions that accommodate wealth effects, and (ii) prices are adjusted discretely via some prefixed increment. A Walrasian equilibrium may not exist in the discrete price setting. We instead propose a novel equilibrium concept, tight equilibrium, that is compatible with discrete prices. A descending-price auction, requiring only partial demand information and featuring a clear price discovery process, is constructed to yield a tight equilibrium. Tight equilibrium ensures efficiency and generalizes the well-known minimum price equilibrium in the continuous price setting to the discrete price setting. We estimate the deviation bound on prices between tight equilibrium and minimum price equilibrium, which depends on the magnitude of wealth effects, the increment size, and the number of objects. Based on this result, we introduce a notion of approximate incentive compatibility and show that our auction is both efficient and approximately incentive compatible.

This paper was accepted by Martin Bichler, market design, platform, and demand analytics.

Funding: Y. Zhou gratefully acknowledges financial support from the National Natural Science Foundation of China [Grant 72394391], the Grant-in-aid for Research Activity, Japan Society for the Promotion of Science [Grants 26H01960 and 22H00062], the Nagoya University Kitankai Fund (2024), and JST ERATO [Grant JPMJER2301].