A Universally Efficient Dynamic Auction for All Unimodular Demand Types

We propose a novel strategy-proof dynamic auction for efficiently allocating heterogeneous indivisible commodities. The auction applies to all unimodular demand types of Baldwin and Klemperer’s necessary and sufficient condition for the existence of competitive equilibrium which accommodate a wide variety of complements, substitutes, gross substitutes and complements, and any other kinds. Although bidders are not assumed to be price takers so they can act strategically, this auction induces bidders to bid truthfully, yielding efficient outcomes. Sincere bidding is shown to be an ex post perfect Nash equilibrium of the auction. The trading rules are simple, detail free, privacy preserving, error tolerant, and independent of any probability distribution assumption. Funding: This work was supported by the Japan Society for the Promotion of Science [Grants 19K11839, and 22K11922] and the Research Institute for Mathematical Sciences at Kyoto University.