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Competitive Equilibria In Matching Models With Financial Constraints

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  • P. Jean‐Jacques Herings
  • Yu Zhou

Abstract

We consider a matching with contracts model in which buyers face financial constraints. In this model, a competitive equilibrium may fail to exist. We therefore propose the new notion of quantity‐constrained competitive equilibrium (QCCE). At a QCCE, buyers form expectations about the expected supply of trades. A buyer may expect that a trade is not to be supplied if the corresponding financial constraint is binding. We show the existence of QCCEs via a dynamic process that updates prices and quantity constraints, the equivalence between QCCE outcomes and stable outcomes, and some other properties of QCCEs like the lattice property.

Suggested Citation

  • P. Jean‐Jacques Herings & Yu Zhou, 2022. "Competitive Equilibria In Matching Models With Financial Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(2), pages 777-802, May.
    • Handle: RePEc:wly:iecrev:v:63:y:2022:i:2:p:777-802
    DOI: 10.1111/iere.12550
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    1. van der Laan, G. & Talman, Dolf & Yang, Z., 2018. "Equilibrium in the Assignment Market under Budget Constraints," Other publications TiSEM 965cd6c8-4f09-47c4-a101-1, Tilburg University, School of Economics and Management.
    2. 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.
    3. Schlegel, Jan Christoph, 2022. "The structure of equilibria in trading networks with frictions," Theoretical Economics, Econometric Society, vol. 17(2), May.
    4. 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.
    5. Elizabeth Baldwin & Omer Edhan & Ravi Jagadeesan & Paul Klemperer & Alexander Teytelboym, 2020. "The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects," Papers 2006.16939, arXiv.org.
    6. Alfred Galichon & Scott Duke Kominers & Simon Weber, 2019. "Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility," Journal of Political Economy, University of Chicago Press, vol. 127(6), pages 2875-2925.
    7. Kucuksenel, Serkan, 2011. "Core of the assignment game via fixed point methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 72-76, January.
    8. Gerard van der Laan & Zaifu Yang, 2016. "An ascending multi-item auction with financially constrained bidders," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 109-149, December.
    9. Tommy Andersson & Lars‐Gunnar Svensson, 2014. "Non‐Manipulable House Allocation With Rent Control," Econometrica, Econometric Society, vol. 82(2), pages 507-539, March.
    10. Herings, P. Jean-Jacques, 2018. "Equilibrium and matching under price controls," Journal of Economic Theory, Elsevier, vol. 177(C), pages 222-244.
    11. Jean-Pascal Benassy, 1975. "Neo-Keynesian Disequilibrium Theory in a Monetary Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(4), pages 503-523.
    12. Gerard van der Laan & Dolf Talman & Zaifu Yang, 2018. "Equilibrium in the Assignment Market under Budget Constraints," Discussion Papers 18/17, Department of Economics, University of York.
    13. Patrick Legros & Andrew F. Newman, 2007. "Beauty Is a Beast, Frog Is a Prince: Assortative Matching with Nontransferabilities," Econometrica, Econometric Society, vol. 75(4), pages 1073-1102, July.
    14. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    15. Talman, Dolf & Yang, Zaifu, 2008. "A dynamic auction for differentiated items under price rigidities," Economics Letters, Elsevier, vol. 99(2), pages 278-281, May.
    16. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    17. Makowski, Louis, 1979. "Value theory with personalized trading," Journal of Economic Theory, Elsevier, vol. 20(2), pages 194-212, April.
    18. 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.
    19. Talman, A.J.J. & Yang, Z.F., 2011. "An Efficient Multi-Item Dynamic Auction with Budget Constrained Bidders," Other publications TiSEM 49292c72-515d-42f4-a0d4-c, Tilburg University, School of Economics and Management.
    20. Talman, A.J.J. & Yang, Z.F., 2007. "A Dynamic Auction for Differentiated Items under Price Rigidities," Other publications TiSEM 34bbf7ff-4bbf-499b-bfd4-3, Tilburg University, School of Economics and Management.
    21. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    22. Jean-Pierre Benoît & Vijay Krishna, 2001. "Multiple-Object Auctions with Budget Constrained Bidders," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(1), pages 155-179.
    23. Patrick Legros & Andrew Newman, 2007. "Beauty is a beast, frog is a prince :assortative matching in a nontransferable world," ULB Institutional Repository 2013/7022, ULB -- Universite Libre de Bruxelles.
    24. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    25. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    26. Kaneko, Mamoru, 1982. "The central assignment game and the assignment markets," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 205-232, September.
    27. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-427, March.
    28. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised May 2018.
    29. A. Talman & Zaifu Yang, 2015. "An efficient multi-item dynamic auction with budget constrained bidders," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 769-784, August.
    30. Dreze, Jacques H, 1975. "Existence of an Exchange Equilibrium under Price Rigidities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(2), pages 301-320, June.
    31. Yeon-Koo Che & Ian Gale, 1998. "Standard Auctions with Financially Constrained Bidders," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 1-21.
    32. Liao, Rose C., 2014. "What drives corporate minority acquisitions around the world? The case for financial constraints," Journal of Corporate Finance, Elsevier, vol. 26(C), pages 78-95.
    33. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    34. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    35. Alkan, Ahmet & Gale, David, 1990. "The core of the matching game," Games and Economic Behavior, Elsevier, vol. 2(3), pages 203-212, September.
    36. Maskin, Eric S., 2000. "Auctions, development, and privatization: Efficient auctions with liquidity-constrained buyers," European Economic Review, Elsevier, vol. 44(4-6), pages 667-681, May.
    37. 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.
    38. Y. Younes, 1975. "On the Role of Money in the Process of Exchange and the Existence of a Non-Walrasian Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(4), pages 489-501.
    39. Talman, A.J.J. & Yang, Z.F., 2008. "A dynamic auction for differentiated items under price rigidity," Other publications TiSEM dbce61c1-07fd-4e95-a9c1-4, Tilburg University, School of Economics and Management.
    40. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    41. Ozan Candogan & Markos Epitropou & Rakesh V. Vohra, 2021. "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Operations Research, INFORMS, vol. 69(1), pages 114-147, January.
    42. Dobzinski, Shahar & Lavi, Ron & Nisan, Noam, 2012. "Multi-unit auctions with budget limits," Games and Economic Behavior, Elsevier, vol. 74(2), pages 486-503.
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    Cited by:

    1. Herings, P. Jean-Jacques & Zhou, Yu, 2021. "Equilibria in Matching Markets with Soft and Hard Liquidity Constraints," Research Memorandum 013, Maastricht University, Graduate School of Business and Economics (GSBE).
    2. Herings, P. Jean-Jacques, 2024. "Expectational equilibria in many-to-one matching models with contracts," Journal of Economic Theory, Elsevier, vol. 216(C).
    3. Elizabeth Baldwin & Omer Edhan & Ravi Jagadeesan & Paul Klemperer & Alexander Teytelboym, 2020. "The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects," Papers 2006.16939, arXiv.org.
    4. Herings, P. Jean-Jacques, 2020. "Expectational Equilibria in Many-to-one Matching Models with Contracts - A Reformulation of Competitive Equilibrium," Research Memorandum 018, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. Hevér, Judit, 2020. "A piaci likviditás és a szabályozás kapcsolatának vizsgálata általános egyensúlyelméleti modellkeretben [The effect of regulation on market liquidity: a general equilibrium approach]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 708-733.

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D45 - Microeconomics - - Market Structure, Pricing, and Design - - - Rationing; Licensing
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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