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Expectational Equilibria in Many-to-one Matching Models with Contracts - A Reformulation of Competitive Equilibrium

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  • Herings, P. Jean-Jacques

    (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics)

Abstract

We introduce the notion of expectational equilibrium in a very general specification of the many-to-one matching with contracts model. The endogenous variables in an expectational equilibrium are expectations about tradable contracts. Expectational equilibrium outcomes are equivalent to stable outcomes. Substitutability of preferences is a sufficient condition for existence. Expectational equilibrium unifies all the other approaches used in the literature so far, in particular Walrasian equilibrium, Drèze equilibrium, and market clearing cutoffs. It also applies to cases where contracts do not involve money as well as cases where there is a smallest monetary unit of account.

Suggested Citation

  • 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).
  • Handle: RePEc:unm:umagsb:2020018
    DOI: 10.26481/umagsb.2020018
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    References listed on IDEAS

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    1. Plott, Charles & Roll, Richard & Seo, Han & Zhao, Hao, 2019. "Tick size, price grids and market performance: Stable matches as a model of market dynamics and equilibrium," Games and Economic Behavior, Elsevier, vol. 118(C), pages 7-28.
    2. 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.
    3. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    4. Talman, Dolf & Yang, Zaifu, 2008. "A dynamic auction for differentiated items under price rigidities," Economics Letters, Elsevier, vol. 99(2), pages 278-281, May.
    5. Herings, P. Jean-Jacques, 2018. "Equilibrium and matching under price controls," Journal of Economic Theory, Elsevier, vol. 177(C), pages 222-244.
    6. 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.
    7. 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.
    8. Kaneko, Mamoru, 1982. "The central assignment game and the assignment markets," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 205-232, September.
    9. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    10. John William Hatfield & Charles R. Plott & Tomomi Tanaka, 2012. "Understanding Price Controls and Nonprice Competition with Matching Theory," American Economic Review, American Economic Association, vol. 102(3), pages 371-375, May.
    11. 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.
    12. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    13. Tommy Andersson & Lars‐Gunnar Svensson, 2014. "Non‐Manipulable House Allocation With Rent Control," Econometrica, Econometric Society, vol. 82(2), pages 507-539, March.
    14. 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.
    15. 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.
    16. Michael Richter & Ariel Rubinstein, 2015. "Back to Fundamentals: Equilibrium in Abstract Economies," American Economic Review, American Economic Association, vol. 105(8), pages 2570-2594, August.
    17. Yuichiro Kamada & Fuhito Kojima, 2015. "Efficient Matching under Distributional Constraints: Theory and Applications," American Economic Review, American Economic Association, vol. 105(1), pages 67-99, January.
    18. 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.
    19. Federico Echenique, 2012. "Contracts versus Salaries in Matching," American Economic Review, American Economic Association, vol. 102(1), pages 594-601, February.
    20. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
    21. Eduardo M. Azevedo & Jacob D. Leshno, 2016. "A Supply and Demand Framework for Two-Sided Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1235-1268.
    22. 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.
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    Cited by:

    1. Andrew MACKENZIE & Yu ZHOU, 2022. "Tract Housing, The Core, And Pendulum Auctions," Discussion papers e-22-005, Graduate School of Economics , Kyoto University.
    2. 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).

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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
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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