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Competition and cooperation in a two-sided matching market with replication

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Abstract

We replicate the “Multiple-partners game” of Sotomayor (1992) to yield a sequence with infinitely many terms. Each term, with more than one stage, is endowed with a structure of subgames given by the previous terms. The concepts of sequential stability and of perfect competitive equilibrium are introduced and characterized. We show that there is a subsequence, such that, for all its terms, these concepts, as well as the traditional concepts of stability and of competitive equilibrium, lead to the same set of allocations, which may be distinct of the core. This not always hold for the terms out of that subsequence.

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  • Sotomayor, Marilda, 2019. "Competition and cooperation in a two-sided matching market with replication," Journal of Economic Theory, Elsevier, vol. 183(C), pages 1030-1056.
    • Handle: RePEc:eee:jetheo:v:183:y:2019:i:c:p:1030-1056
    DOI: 10.1016/j.jet.2019.07.013
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    References listed on IDEAS

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    1. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    2. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    3. Sotomayor, Marilda, 2007. "Connecting the cooperative and competitive structures of the multiple-partners assignment game," Journal of Economic Theory, Elsevier, vol. 134(1), pages 155-174, May.
    4. 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.
    5. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    6. Eyal Winter & Myrna Wooders, 2008. "On large games with bounded essential coalition sizes," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(2), pages 191-206, June.
    7. Marilda Sotomayor, 1992. "The Multiple Partners Game," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 17, pages 322-354, Palgrave Macmillan.
    8. Marilda Sotomayor, 2009. "Adjusting prices in the multiple-partners assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 575-600, November.
    9. Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 567-583.
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    More about this item

    Keywords

    Sequential stability; Perfect competitive equilibrium; Equal treatment property; Sequential games; Extended markets; Core;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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