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Gross substitutes and endowed assignment valuations

Author

Listed:
  • Ostrovsky, Michael

    (Graduate School of Business, Stanford University)

  • Paes Leme, Renato

    (Google Research)

Abstract

We show that the class of preferences satisfying the Gross Substitutes condition of Kelso and Crawford (1982) is strictly larger than the class of Endowed Assignment Valuations of Hatfield and Milgrom (2005), thus resolving the open question posed by the latter paper. In particular, our result implies that not every substitutable valuation function can be "decomposed" into a combination of unit-demand valuations.

Suggested Citation

  • Ostrovsky, Michael & Paes Leme, Renato, 2015. "Gross substitutes and endowed assignment valuations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    • Handle: RePEc:the:publsh:1840
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    References listed on IDEAS

    as
    1. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    2. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 639-645.
    3. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
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    6. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    7. Kazuo Murota & Akiyoshi Shioura, 1999. "M-Convex Function on Generalized Polymatroid," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 95-105, February.
    8. John William Hatfield & Scott Duke Kominers & Alexandru Nichifor & Michael Ostrovsky & Alexander Westkamp, 2013. "Stability and Competitive Equilibrium in Trading Networks," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 966-1005.
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    11. Lehmann, Benny & Lehmann, Daniel & Nisan, Noam, 2006. "Combinatorial auctions with decreasing marginal utilities," Games and Economic Behavior, Elsevier, vol. 55(2), pages 270-296, May.
    12. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
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    Citations

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    Cited by:

    1. Delacrétaz, David & Loertscher, Simon & Marx, Leslie M. & Wilkening, Tom, 2019. "Two-sided allocation problems, decomposability, and the impossibility of efficient trade," Journal of Economic Theory, Elsevier, vol. 179(C), pages 416-454.
    2. Fichtl, Maximilian, 2021. "On the expressiveness of assignment messages," Economics Letters, Elsevier, vol. 208(C).
    3. Klemperer, Paul & Baldwin, Elizabeth & Edhan, Omer & Jagadeesan, Ravi & Teytelboym, Alexander, 2020. "The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects," CEPR Discussion Papers 14926, C.E.P.R. Discussion Papers.
    4. Paes Leme, Renato, 2017. "Gross substitutability: An algorithmic survey," Games and Economic Behavior, Elsevier, vol. 106(C), pages 294-316.
    5. Kazuo Murota, 2016. "Discrete convex analysis: A tool for economics and game theory," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 151-273, December.
    6. Huang, Chao, 2018. "Independence systems in gross-substitute valuations," Economics Letters, Elsevier, vol. 173(C), pages 135-137.
    7. 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.

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    More about this item

    Keywords

    Substitutability; matching; combinatorial auctions; matroids;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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