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

Author

Listed:
  • Elizabeth Baldwin

    (Dept of Economics, Oxford University)

  • Martin Bichler

    (Dept of Computer Science, Technical University of Munich)

  • Maximilian Fichtl

    (Dept of Computer Science, Technical University of Munich)

  • Paul Klemperer

    (Dept of Economics, Oxford University)

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

  • Elizabeth Baldwin & Martin Bichler & Maximilian Fichtl & Paul Klemperer, 2021. "Strong Substitutes: Structural Properties, and a New Algorithm for Competitive Equilibrium Prices," Economics Papers 2021-W02, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:2102
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    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

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