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Gross substitutes and complements: A simple generalization

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  • Teytelboym, Alexander

Abstract

We extend the gross substitutes and complements framework (Sun and Yang, 2006). Competitive equilibrium with indivisible goods exists under significantly weaker, intuitive and interpretable conditions. A generalized dynamic double-track procedure (Sun and Yang, 2008, 2009) finds the competitive equilibrium outcome.

Suggested Citation

  • Teytelboym, Alexander, 2014. "Gross substitutes and complements: A simple generalization," Economics Letters, Elsevier, vol. 123(2), pages 135-138.
    • Handle: RePEc:eee:ecolet:v:123:y:2014:i:2:p:135-138
    DOI: 10.1016/j.econlet.2014.01.038
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    1. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    2. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
    3. Ning Sun & Zaifu Yang, 2008. "A Double-Track Auction for Substitutes and Complements," KIER Working Papers 656, Kyoto University, Institute of Economic Research.
    4. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    5. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    6. Ning Sun & Zaifu Yang, 2009. "A Double-Track Adjustment Process for Discrete Markets With Substitutes and Complements," Econometrica, Econometric Society, vol. 77(3), pages 933-952, May.
    7. Hitoshi Matsushima, 2012. ""4G Spectrum Auction in Japan: Japanese Package Auction (JPA)" (in Japanese)," CIRJE J-Series CIRJE-J-240, CIRJE, Faculty of Economics, University of Tokyo.
    8. Talman, Dolf & Yang, Zaifu, 2011. "A model of partnership formation," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 206-212, March.
    9. Milgrom, Paul & Strulovici, Bruno, 2009. "Substitute goods, auctions, and equilibrium," Journal of Economic Theory, Elsevier, vol. 144(1), pages 212-247, January.
    10. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    11. 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.
    12. Gudmundsson, Jens, 2013. "Cycles and Third-Party Payments in the Partnership Formation Problem," Working Papers 2013:16, Lund University, Department of Economics.
    13. Akiyoshi Shioura & Zaifu Yang, 2013. "Equilibrium, Auction, Multiple Substitutes and Complements," Discussion Papers 13/17, Department of Economics, University of York.
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    Cited by:

    1. Masahiro KAWASAKI & Ryosuke SAKAI & Tomoya KAZUMURA, 2023. "Sequential dictatorship rules in multi-unit objectassignment problems with money," Discussion papers e-23-007, Graduate School of Economics , Kyoto University.
    2. 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.
    3. Sun, Ning & Yang, Zaifu, 2016. "An Efficient and Strategy-Proof Double-Track Auction for Substitutes and Complements," Center for Mathematical Economics Working Papers 523, Center for Mathematical Economics, Bielefeld University.
    4. Bernhard Kasberger & Alexander Teytelboym, 2022. "The Combinatorial Multi-Round Ascending Auction," Papers 2203.11783, arXiv.org, revised Feb 2024.
    5. 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.
    6. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    7. Yang, Yi-You, 2013. "Competitive equilibrium with indivisible objects," MPRA Paper 74662, University Library of Munich, Germany, revised 19 Oct 2016.
    8. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised May 2018.

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    More about this item

    Keywords

    Indivisibilities; Competitive equilibrium; Gross substitutes and complements; Auctions;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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