DP15831 Strong Substitutes: Structural Properties, and a New Algorithm for Competitive Equilibrium Prices

Author(s): Elizabeth Baldwin, Martin Bichler, Maximilian Fichtl, Paul Klemperer
Publication Date: February 2021
Keyword(s): Algorithms, Auction Theory, Competitive Equilibrium, DC programming, Envy-free prices, Equilibrium computation, indivisible goods, product-mix auction, strong substitutes, Walrasian Equilibrium
JEL(s):
Programme Areas: Financial Economics, Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=15831

We show the Strong Substitutes Product-Mix Auction (SSPMA) bidding language provides an intuitive and geometric interpretation of strong substitutes as Minkowski differences between sets that are easy to identify.We prove that competitive equilibrium prices for agents with strong substitutes preferences can be computed by minimizing the difference between two linear programs for the positive and the negative bids with suitably relaxed resource constraints. This also leads to a new algorithm for computing competitive equilibrium prices which is competitive with standard steepest descent algorithms in extensive experiments.