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Assortative Matching with Externalities and Farsighted Agents

Author

Listed:
  • Kenzo Imamura

    (The University of Tokyo Market Design Center)

  • Hideo Konishi

    (Boston College)

Abstract

We consider a one-to-one assortative matching problem in which matched pairs compete for a prize. With externalities, the standard solution concept—pairwise stable matching—may not exist. In this paper, we consider farsighted agents and analyze the largest consistent set (LCS) of Chwe (J Econ Theory 63:299-325, 1994). Despite the assortative structure of the problem, LCS tend to be large with the standard effectiveness functions: LCS can be the set of all matchings, including an empty matching with no matched pair. By modifying the effectiveness function motivated by Knuth (Marriages stables. Les Presses de l’Universite de Montreal, Montreal, 1976), LCS becomes a singleton of the positive assortative matching. Our results suggest that the choice of the effectiveness function can significantly impact the solution for a matching problem with externalities.

Suggested Citation

  • Kenzo Imamura & Hideo Konishi, 2023. "Assortative Matching with Externalities and Farsighted Agents," Dynamic Games and Applications, Springer, vol. 13(2), pages 497-509, June.
    • Handle: RePEc:spr:dyngam:v:13:y:2023:i:2:d:10.1007_s13235-022-00462-y
    DOI: 10.1007/s13235-022-00462-y
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    as
    1. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    2. , & , J. & ,, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    3. Imamura, Kenzo & Konishi, Hideo & Pan, Chen-Yu, 2023. "Stability in matching with externalities: Pairs competition and oligopolistic joint ventures," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 270-286.
    4. Debraj Ray & Rajiv Vohra, 2015. "The Farsighted Stable Set," Econometrica, Econometric Society, vol. 83(3), pages 977-1011, May.
    5. Bo Chen, 2019. "Downstream competition and upstream labor market matching," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1055-1085, December.
    6. Dutta, Bhaskar & Vohra, Rajiv, 2017. "Rational expectations and farsighted stability," Theoretical Economics, Econometric Society, vol. 12(3), September.
    7. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    8. Debraj Ray & Rajiv Vohra, 2019. "Maximality in the Farsighted Stable Set," Econometrica, Econometric Society, vol. 87(5), pages 1763-1779, September.
    9. Sasaki, Hiroo & Toda, Manabu, 1996. "Two-Sided Matching Problems with Externalities," Journal of Economic Theory, Elsevier, vol. 70(1), pages 93-108, July.
    10. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
    11. Fisher, James C.D. & Hafalir, Isa E., 2016. "Matching with aggregate externalities," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 1-7.
    12. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, V., 2020. "Do Stable Outcomes Survive in Marriage Problems with Myopic and Farsighted Players?," Research Memorandum 031, Maastricht University, Graduate School of Business and Economics (GSBE).
    13. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July.
    14. Marek Pycia & M Bumin Yenmez, 2023. "Matching with Externalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(2), pages 948-974.
    15. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 39-61, August.
    16. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    17. Dutta, Bhaskar & Vartiainen, Hannu, 2020. "Coalition formation and history dependence," Theoretical Economics, Econometric Society, vol. 15(1), January.
    18. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
    19. Kimya, Mert, 2020. "Farsighted Objections and Maximality in One-to-one Matching Problems," Working Papers 202014, University of Sydney, School of Economics, revised Jul 2021.
    20. 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.
    21. 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.
    22. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    23. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    24. Mumcu, Ayse & Saglam, Ismail, 2010. "Stable one-to-one matchings with externalities," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 154-159, September.
    25. Francis Bloch & Santiago Sánchez-Pagés & Raphaël Soubeyran, 2006. "When does universal peace prevail? Secession and group formation in conflict," Economics of Governance, Springer, vol. 7(1), pages 3-29, January.
    26. Carraro,Carlo & Siniscalco,Domenico (ed.), 1997. "New Directions in the Economic Theory of the Environment," Cambridge Books, Cambridge University Press, number 9780521590891, September.
    27. Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 473-488, March.
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    More about this item

    Keywords

    Group contest; Pairwise stable matching; Assortative matching; Farsightedness; Largest consistent set; Effectiveness function;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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