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Computing a Walrasian Equilibrium in Iterative Auctions with Multiple Differentiated Items

Author

Listed:
  • Kazuo Murota
  • Akiyoshi Shioura
  • Zaifu Yang

Abstract

We address the problem of computing a Walrasian equilibrium price in an ascending auction with gross substitutes valuations. In particular, an auction market is considered where there are multiple differentiated goods and each good may have multiple units. Although the ascending auction is known to ï¬ nd an equilibrium price vector in ï¬ nite time, little is known about its time complexity. The main aim of this paper is to analyze the time complexity of the ascending auction globally and locally, by utilizing the theory of discrete convex analysis. An exact bound on the number of iterations is given in terms of the L infinity distance between the initial price vector and an equilibrium, and an efficient algorithm to update a price vector is designed based on a min-max theorem for submodular function minimization.

Suggested Citation

  • Kazuo Murota & Akiyoshi Shioura & Zaifu Yang, 2013. "Computing a Walrasian Equilibrium in Iterative Auctions with Multiple Differentiated Items," Discussion Papers 13/13, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:13/13
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    Citations

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    Cited by:

    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. Goko, Hiromichi & Igarashi, Ayumi & Kawase, Yasushi & Makino, Kazuhisa & Sumita, Hanna & Tamura, Akihisa & Yokoi, Yu & Yokoo, Makoto, 2024. "A fair and truthful mechanism with limited subsidy," Games and Economic Behavior, Elsevier, vol. 144(C), pages 49-70.
    3. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.

    More about this item

    Keywords

    Dynamic auction; gross substitutes; equilibrium; complexity;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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