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Matching With Complementary Contracts

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  • Marzena Rostek
  • Nathan Yoder

Abstract

In this paper, we show that stable outcomes exist in matching environments with complementarities, such as social media platforms or markets for patent licenses. Our results apply to both nontransferable and transferable utility settings, and allow for multilateral agreements and those with externalities. In particular, we show that stable outcomes in these settings are characterized by the largest fixed point of a monotone operator, and so can be found using an algorithm; in the nontransferable utility case, this is a one‐sided deferred acceptance algorithm, rather than a Gale–Shapley algorithm. We also give a monotone comparative statics result as well as a comparative static on the effect of bundling contracts together. These illustrate the impact of design decisions, such as increased privacy protections on social media, or the use of antitrust law to disallow patent pools, on stable outcomes.

Suggested Citation

  • Marzena Rostek & Nathan Yoder, 2020. "Matching With Complementary Contracts," Econometrica, Econometric Society, vol. 88(5), pages 1793-1827, September.
    • Handle: RePEc:wly:emetrp:v:88:y:2020:i:5:p:1793-1827
    DOI: 10.3982/ECTA16686
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    References listed on IDEAS

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    2. Bando, Keisuke & Hirai, Toshiyuki, 2021. "Stability and venture structures in multilateral matching," Journal of Economic Theory, Elsevier, vol. 196(C).
    3. Marco LiCalzi, 2022. "Bipartite choices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 551-568, December.
    4. Chao Huang, 2023. "Multilateral matching with scale economies," Papers 2310.19479, arXiv.org.
    5. Danilov, Vladimir I. & Karzanov, Alexander V., 2023. "Stable and meta-stable contract networks," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    6. Umut Dur & Thayer Morrill & William Phan, 2024. "Partitionable choice functions and stability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(2), pages 359-375, September.
    7. SHINOZAKI, Hiroki, 2023. "Non-obvious manipulability and efficiency in package assignment problems with money for agents with income effects and hard budget constraints," Discussion paper series HIAS-E-136, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    8. Chao Huang, 2022. "Firm-worker hypergraphs," Papers 2211.06887, arXiv.org, revised Nov 2023.
    9. Chao Huang, 2023. "Concave many-to-one matching," Papers 2309.04181, arXiv.org.
    10. Marek Pycia & M Bumin Yenmez, 2023. "Matching with Externalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(2), pages 948-974.
    11. Ravi Jagadeesan & Alexander Teytelboym, 2024. "The Economics of Equilibrium with Indivisible Goods," Papers 2412.07946, arXiv.org.
    12. Chao Huang, 2022. "Two-sided matching with firms' complementary preferences," Papers 2205.05599, arXiv.org, revised May 2022.
    13. Tarun Sabarwal, 2023. "Universal Theory of Equilibrium in Models with Complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202312, University of Kansas, Department of Economics, revised Nov 2023.
    14. Di Feng, 2023. "Endowments-swapping-proofness and Efficiency in Multiple-Type Housing Markets," Discussion Paper Series DP2023-14, Research Institute for Economics & Business Administration, Kobe University.
    15. Di Feng, 2023. "Efficiency in Multiple-Type Housing Markets," Papers 2308.14989, arXiv.org, revised Dec 2023.
    16. Vladimir Danilov, 2022. "Complementary choice functions," Papers 2209.06514, arXiv.org.
    17. Chao Huang, 2024. "A dynamic auction for multilateral collaboration," Papers 2411.06545, arXiv.org.
    18. Yokote, Koji, 2023. "A critical comparison between the gross substitutes and complements conditions," Economics Letters, Elsevier, vol. 226(C).

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