DP14976 Solving Strong-Substitutes Product-Mix Auctions

Author(s): Elizabeth Baldwin, Paul Goldberg, Paul Klemperer, Edwin Lock
Publication Date: June 2020
Keyword(s): bidding language, Competitive Equilibrium, convex optimisation, product-mix auction, strong substitutes, submodular minimisation, Walrasian Equilibrium
JEL(s): D44
Programme Areas: Financial Economics, Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=14976

This paper develops algorithms to solve strong-substitutes product-mix auctions: it finds competitive equilibrium prices and quantities for agents who use this auction's bidding language to truthfully express their strong-substitutes preferences over an arbitrary number of goods, each of which is available in multiple discrete units. Our use of the bidding language, and the information it provides, contrasts with existing algorithms that rely on access to a valuation or demand oracle. We compute market-clearing prices using algorithms that apply existing submodular minimisation methods. Allocating the supply among the bidders at these prices then requires solving a novel constrained matching problem. Our algorithm iteratively simplifies the allocation problem, perturbing bids and prices in a way that resolves tie-breaking choices created by bids that can be accepted on more than one good. We provide practical running time bounds on both price-finding and allocation, and illustrate experimentally that our allocation mechanism is practical.