A Universal Dynamic Auction for Unimodular Demand Types: An Efficient Auction Design for Various Kinds of Indivisible Commodities

Abstract

We propose a new and general dynamic design for efficiently auctioning multiple heterogeneous indivisible items. The auction applies to all unimodular demand types of Baldwin and Klemperer (2019) which are a necessary and sufficient condition for the existence of competitive equilibrium in economies with indivisible goods and accommodate a variety of substitutes, complements, gross substitutes and complements, strong substitutes, and other kinds. Every bidder has private valuation on each of his interested bundles of items and the seller has a reserve price for every bundle of items. The auctioneer announces the current prices for all items, bidders respond by reporting their demands at these prices, and then the auctioneer adjusts the prices of items. The trading rules are simple, transparent, and detail-free. Although bidders are not assumed to be price-takers so they can strategically exercise their market power, this auction induces bidders to bid truthfully and yields an e cient outcome. Bidding sincerely is an ex post perfect Nash equilibrium. The auction is also privacypreserving and independent of any probability distribution assumption.