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Verifying gross substitutability

Author

Listed:
  • Jos A.M. Potters

    (Department of Mathematics, Nijmegen University, P.O. Box 9010,6500 GL Nijmegen,THE NETHERLANDS)

  • Anita van Gellekom

    (Department of Mathematics, Nijmegen University, P.O. Box 9010,6500 GL Nijmegen,THE NETHERLANDS)

  • Hans Reijnierse

    (Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, THE NETHERLANDS .)

Abstract

In labor market models as well as in exchange economies with indivisible goods gross substitutability is used as a property to guarantee the existence of competitive equilibria. This paper develops an easy way to check gross substitutability for utility functions concerning a finite set of indivisible goods (or employees) and money. Concavity is one of the conditions that has to be satisfied. Only one other, but similar, type of relation must be checked to guarantee gross substitutability.

Suggested Citation

  • Jos A.M. Potters & Anita van Gellekom & Hans Reijnierse, 2002. "Verifying gross substitutability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 767-776.
    • Handle: RePEc:spr:joecth:v:20:y:2002:i:4:p:767-776
    Note: Received: 21 August 2000; revised version: 28 November 2001
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    Citations

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    Cited by:

    1. Ostrovsky, Michael & Paes Leme, Renato, 2015. "Gross substitutes and endowed assignment valuations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    2. Kumar, Ujjwal & Roy, Souvik, 2024. "Local incentive compatibility on gross substitutes and other non-convex type-spaces," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    3. Goossens, D.R. & Müller, R.J. & Spieksma, F.C.R., 2007. "Matrix bids in combinatorial auctions: expressiveness and micro-economic properties," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 639-645.
    5. Saurabh Amin & Patrick Jaillet & Haripriya Pulyassary & Manxi Wu, 2023. "Market Design for Dynamic Pricing and Pooling in Capacitated Networks," Papers 2307.03994, arXiv.org, revised Nov 2023.
    6. Yang, Yi-You, 2013. "Competitive equilibrium for indivisible objects," MPRA Paper 57637, University Library of Munich, Germany, revised 28 Jul 2014.
    7. Roy, Souvik & Kumar, Ujjwal, 2021. "Local incentive compatibility in non-convex type-spaces," MPRA Paper 110872, University Library of Munich, Germany.
    8. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    9. Yang, Yi-You, 2013. "Competitive equilibrium with indivisible objects," MPRA Paper 74662, University Library of Munich, Germany, revised 19 Oct 2016.
    10. Yang, Yi-You, 2013. "A classification approach to Walrasian equilibrium with substitutability," MPRA Paper 47945, University Library of Munich, Germany.
    11. Dries R. Goossens & Rudolf Müller & Frits C. R. Spieksma, 2010. "Algorithms for Recognizing Economic Properties in Matrix Bid Combinatorial Auctions," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 339-352, August.
    12. Eric Balkanski & Renato Paes Leme, 2020. "On the Construction of Substitutes," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 272-291, February.
    13. Paes Leme, Renato, 2017. "Gross substitutability: An algorithmic survey," Games and Economic Behavior, Elsevier, vol. 106(C), pages 294-316.
    14. 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.
    15. Hatfield, John William & Kominers, Scott Duke & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2019. "Full substitutability," Theoretical Economics, Econometric Society, vol. 14(4), November.
    16. Huang, Chao, 2018. "Independence systems in gross-substitute valuations," Economics Letters, Elsevier, vol. 173(C), pages 135-137.
    17. Ben-Zwi, Oren, 2017. "Walrasian's characterization and a universal ascending auction," Games and Economic Behavior, Elsevier, vol. 104(C), pages 456-467.
    18. Kazuo Murota & Yu Yokoi, 2015. "On the Lattice Structure of Stable Allocations in a Two-Sided Discrete-Concave Market," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 460-473, February.

    More about this item

    Keywords

    Gross substitutability; Competitive equilibrium; Labor market; Exchange economies with indivisible goods.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • J40 - Labor and Demographic Economics - - Particular Labor Markets - - - General

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