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A critical comparison between the gross substitutes and complements conditions

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  • Yokote, Koji

Abstract

In a transferable utility matching environment, the gross substitutes condition (Kelso and Crawford 1982) and the gross complements condition (Rostek and Yodar 2020) guarantee the existence of equilibrium outcomes. We show that the difference between the two conditions is pinpointed to the direction of price changes: the former condition requires that any set of demanded contracts is still demanded after the prices of other contracts increase, while the latter condition requires that any set of demanded contracts is still demanded after the prices of other contracts decrease.

Suggested Citation

  • Yokote, Koji, 2023. "A critical comparison between the gross substitutes and complements conditions," Economics Letters, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:ecolet:v:226:y:2023:i:c:s0165176523001313
    DOI: 10.1016/j.econlet.2023.111106
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    References listed on IDEAS

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    1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    2. Marzena Rostek & Nathan Yoder, 2020. "Matching With Complementary Contracts," Econometrica, Econometric Society, vol. 88(5), pages 1793-1827, September.
    3. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    4. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    5. 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.
    6. Hatfield, John William & Kominers, Scott Duke & Nichifor, Alexandru & Ostrovsky, Michael & Westkamp, Alexander, 2019. "Full substitutability," Theoretical Economics, Econometric Society, vol. 14(4), November.
    7. Satoru Fujishige & Zaifu Yang, 2003. "A Note on Kelso and Crawford's Gross Substitutes Condition," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 463-469, August.
    8. Fuhito Kojima & Ning Sun & Ning Neil Yu, 2020. "Job Matching under Constraints," American Economic Review, American Economic Association, vol. 110(9), pages 2935-2947, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Matching; Equilibrium existence; Gross substitutability; Gross complementarity;
    All these keywords.

    JEL classification:

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

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