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A modified deferred acceptance algorithm for many-to-one matching markets with externalities among firms

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  • Bando, Keisuke

Abstract

We consider a many-to-one matching market with externalities among firms where each firm’s preferences satisfy substitutability, increasing choice and no external effect by unchosen workers, which are defined by Bando (2012). We first illustrate that a sequential version of the deferred acceptance (DA) algorithm with worker-proposing may not find a worker-optimal quasi stable matching. Then, we provide a modified DA algorithm in which (i) each worker simultaneously proposes to his most preferred firm that has not rejected him and (ii) each firm chooses its acceptable workers from the cumulative set of workers who have ever proposed to it, assuming that the other workers proposing to its rival firms are hired. We show that this algorithm finds a worker-optimal quasi stable matching. We also show that this algorithm can be generalized into a fixed point algorithm.

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  • Bando, Keisuke, 2014. "A modified deferred acceptance algorithm for many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 173-181.
    • Handle: RePEc:eee:mateco:v:52:y:2014:i:c:p:173-181
    DOI: 10.1016/j.jmateco.2014.01.001
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    7. Fisher, James C.D., 2020. "Existence of stable allocations in matching markets with infinite contracts: A topological approach," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 136-140.
    8. José Luis Contreras & Juan Pablo Torres-Martínez, 2021. "The roommate problem with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 149-165, March.
    9. Ayse Mumcu & Ismail Saglam, 2019. "Strategic Issues in One-to-One Matching with Externalities Abstract:," Working Papers 2019/03, Bogazici University, Department of Economics.
    10. Kenzo Imamura & Hideo Konishi, 2023. "Assortative Matching with Externalities and Farsighted Agents," Dynamic Games and Applications, Springer, vol. 13(2), pages 497-509, June.
    11. AyÅŸe Mumcu & Ismail Saglam, 2021. "Strategic Issues in One-to-One Matching with Externalities," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 23(02), pages 1-12, June.
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