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

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  • Klemperer, Paul
  • Baldwin, Elizabeth
  • Bichler, Martin
  • Fichtl, Maximilian

Abstract

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.

Suggested Citation

  • Klemperer, Paul & Baldwin, Elizabeth & Bichler, Martin & Fichtl, Maximilian, 2021. "Strong Substitutes: Structural Properties, and a New Algorithm for Competitive Equilibrium Prices," CEPR Discussion Papers 15831, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:15831
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    1. Elizabeth Baldwin & Paul W. Goldberg & Paul Klemperer & Edwin Lock, 2019. "Solving Strong-Substitutes Product-Mix Auctions," Economics Papers 2019-W08, Economics Group, Nuffield College, University of Oxford.
    2. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    3. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    4. Martin Bichler & Pasha Shabalin & Georg Ziegler, 2013. "Efficiency with Linear Prices? A Game-Theoretical and Computational Analysis of the Combinatorial Clock Auction," Information Systems Research, INFORMS, vol. 24(2), pages 394-417, June.
    5. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
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