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Matching in Networks with Bilateral Contracts

Author

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  • John William Hatfield
  • Scott Duke Kominers

Abstract

We introduce a model in which firms trade goods via bilateral contracts which specify a buyer, a seller, and the terms of the exchange. This setting subsumes (many-to-many) matching with contracts, as well as supply chain matching. When firms' relationships do not exhibit a supply chain structure, stable allocations need not exist. By contrast, in the presence of supply chain structure, a natural substitutability condition characterizes the maximal domain of firm preferences for which stable allocations are guaranteed to exist. Furthermore, the classical lattice structure, rural hospitals theorem, and one-sided strategy-proofness results all generalize to this setting. (JEL C78, D85, D86, L14)

Suggested Citation

  • John William Hatfield & Scott Duke Kominers, 2012. "Matching in Networks with Bilateral Contracts," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 176-208, February.
  • Handle: RePEc:aea:aejmic:v:4:y:2012:i:1:p:176-208
    Note: DOI: 10.1257/mic.4.1.176
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    References listed on IDEAS

    as
    1. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    2. 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.
    3. Westkamp, Alexander, 2010. "Market structure and matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1724-1738, September.
    4. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    5. Kojima, Fuhito, 2008. "The law of aggregate demand and welfare in the two-sided matching market," Economics Letters, Elsevier, vol. 99(3), pages 581-584, June.
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    7. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    8. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    9. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    10. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, vol. 129(1), pages 57-80, July.
    11. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    12. John William Hatfield & Fuhito Kojima, 2008. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 98(3), pages 1189-1194, June.
    13. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    14. Sotomayor, Marilda, 2004. "Implementation in the many-to-many matching market," Games and Economic Behavior, Elsevier, vol. 46(1), pages 199-212, January.
    15. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. repec:eee:gamebe:v:108:y:2018:i:c:p:275-286 is not listed on IDEAS
    2. Sonja Brangewitz & Claus-Jochen Haake & Philipp Moehlmeier, 2015. "Strategic Formation of Customer Relationship Networks," Working Papers CIE 91, Paderborn University, CIE Center for International Economics.
    3. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised May 2018.
    4. repec:eee:gamebe:v:108:y:2018:i:c:p:287-294 is not listed on IDEAS
    5. Herings P.J.J., 2015. "Equilibrium and matching under price controls," Research Memorandum 001, Maastricht University, Graduate School of Business and Economics (GSBE).
    6. Francis Bloch & David Cantala & Damián Gibaja, 2017. "Matching through institutions," Serie documentos de trabajo del Centro de Estudios Económicos 2017-03, El Colegio de México, Centro de Estudios Económicos.
    7. Bernard Salanié & Alfred Galichon, 2012. "Cupid's Invisible Hand: Social Surplus and Identification in Matching Models," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
    8. repec:eee:jetheo:v:176:y:2018:i:c:p:803-833 is not listed on IDEAS
    9. Kominers, Scott Duke, 2012. "On the correspondence of contracts to salaries in (many-to-many) matching," Games and Economic Behavior, Elsevier, vol. 75(2), pages 984-989.
    10. Nava, Francesco, 2015. "Efficiency in decentralized oligopolistic markets," Journal of Economic Theory, Elsevier, vol. 157(C), pages 315-348.
    11. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    12. Hatfield, John William & Immorlica, Nicole & Kominers, Scott Duke, 2012. "Testing substitutability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 639-645.
    13. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    14. repec:eee:ecolet:v:156:y:2017:i:c:p:65-67 is not listed on IDEAS
    15. Hatfield, John William & Kominers, Scott Duke, 2015. "Multilateral matching," Journal of Economic Theory, Elsevier, vol. 156(C), pages 175-206.
    16. repec:eee:mateco:v:72:y:2017:i:c:p:104-111 is not listed on IDEAS
    17. Kadam, Sangram Vilasrao, 2017. "Unilateral substitutability implies substitutable completability in many-to-one matching with contracts," Games and Economic Behavior, Elsevier, vol. 102(C), pages 56-68.
    18. repec:oup:oxford:v:33:y:2017:i:4:p:541-571. is not listed on IDEAS
    19. Tayfun Sönmez & Tobias B. Switzer, 2013. "Matching With (Branch‐of‐Choice) Contracts at the United States Military Academy," Econometrica, Econometric Society, vol. 81(2), pages 451-488, March.
    20. Hatfield, John William & Kominers, Scott Duke, 2013. "Vacancies in supply chain networks," Economics Letters, Elsevier, vol. 119(3), pages 354-357.
    21. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press, vol. 33(4), pages 541-571.
    22. Hatfield, John William & Plott, Charles R. & Tanaka, Tomomi, 2016. "Price controls, non-price quality competition, and the nonexistence of competitive equilibrium," Games and Economic Behavior, Elsevier, vol. 99(C), pages 134-163.
    23. Quint, Daniel, 2014. "Imperfect competition with complements and substitutes," Journal of Economic Theory, Elsevier, vol. 152(C), pages 266-290.

    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

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