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Stable matching and protocol-free equilibrium

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  • Okada, Akira

Abstract

We consider a non-cooperative decentralized matching game as sequential bargaining. A protocol-free equilibrium is a subgame perfect equilibrium which is robust to a choice of a bargaining protocol. We show that a matching is generated in a protocol-free equilibrium if and only if it is stable. The bargaining game can be applied to a wide class of matching problems including marriage problems, college admissions problems, matching with contracts, assignment games, and cooperative NTU games.

Suggested Citation

  • Okada, Akira, 2021. "Stable matching and protocol-free equilibrium," Games and Economic Behavior, Elsevier, vol. 128(C), pages 193-201.
    • Handle: RePEc:eee:gamebe:v:128:y:2021:i:c:p:193-201
    DOI: 10.1016/j.geb.2021.04.006
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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Perry, Motty & Reny, Philip J, 1994. "A Noncooperative View of Coalition Formation and the Core," Econometrica, Econometric Society, vol. 62(4), pages 795-817, July.
    3. Thomas Demuynck & P. Jean‐Jacques Herings & Riccardo D. Saulle & Christian Seel, 2019. "The Myopic Stable Set for Social Environments," Econometrica, Econometric Society, vol. 87(1), pages 111-138, January.
    4. , & , J. & ,, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    5. Guillaume Haeringer & Myrna Wooders, 2011. "Decentralized job matching," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(1), pages 1-28, February.
    6. Herings, P. Jean-Jacques, 2018. "Equilibrium and matching under price controls," Journal of Economic Theory, Elsevier, vol. 177(C), pages 222-244.
    7. Alcalde, Jose & Romero-Medina, Antonio, 2000. "Simple Mechanisms to Implement the Core of College Admissions Problems," Games and Economic Behavior, Elsevier, vol. 31(2), pages 294-302, May.
    8. Akira Okada & Eyal Winter, 2002. "A Non-cooperative Axiomatization of the Core," Theory and Decision, Springer, vol. 53(1), pages 1-28, August.
    9. Alcalde, Jose & Perez-Castrillo, David & Romero-Medina, Antonio, 1998. "Hiring Procedures to Implement Stable Allocations," Journal of Economic Theory, Elsevier, vol. 82(2), pages 469-480, October.
    10. Francis Bloch & Effrosyni Diamantoudi, 2011. "Noncooperative formation of coalitions in hedonic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 263-280, May.
    11. Kamecke, U, 1989. "Non-cooperative Matching Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 423-431.
    12. Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Stable sets in matching problems with coalitional sovereignty and path dominance," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 14-19.
    13. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    14. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2015. "Decentralized matching: The role of commitment," Games and Economic Behavior, Elsevier, vol. 92(C), pages 1-17.
    15. Jean-Jacques HERINGS & Ana MAULEON & Vincent VANNETELBOSCH, 2017. "Stable sets in matching problems with coalitional sovereignty path dominance," LIDAM Reprints CORE 2861, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    17. John William Hatfield & Fuhito Kojima, 2008. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 98(3), pages 1189-1194, June.
    18. Konishi, Hideo & Sapozhnikov, Margarita, 2008. "Decentralized matching markets with endogenous salaries," Games and Economic Behavior, Elsevier, vol. 64(1), pages 193-218, September.
    19. 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.
    20. Yujiro Kawasaki, 2013. "One-to-many non-cooperative matching games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 521-539, May.
    21. Moldovanu Benny & Winter Eyal, 1995. "Order Independent Equilibria," Games and Economic Behavior, Elsevier, vol. 9(1), pages 21-34, April.
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    More about this item

    Keywords

    Decentralized market; Many-to-one matching; Protocol-free equilibrium; Sequential bargaining; Stability;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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