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Search theory, competitive equilibrium, and the Nash bargaining solution

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  • Cho, In-Koo
  • Matsui, Akihiko

Abstract

We investigate a canonical search-theoretic model without entry. Two agents are randomly matched with a long side being rationed. The matched agents face a pair of randomly drawn non-transferable payoffs, and then choose whether or not to form a partnership subject to a small probability of exogenous break down. As this probability and friction vanish, the Nash bargaining solution emerges as the unique undominated strategy equilibrium outcome if the mass of each party is the same. If the size of one party is larger than the other, the short side extracts the entire surplus, a sharp contrast to Rubinstein and Wolinsky (1985) [16].

Suggested Citation

  • Cho, In-Koo & Matsui, Akihiko, 2013. "Search theory, competitive equilibrium, and the Nash bargaining solution," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1659-1688.
  • Handle: RePEc:eee:jetheo:v:148:y:2013:i:4:p:1659-1688
    DOI: 10.1016/j.jet.2013.04.003
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    References listed on IDEAS

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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. Stephan Lauermann, 2013. "Dynamic Matching and Bargaining Games: A General Approach," American Economic Review, American Economic Association, vol. 103(2), pages 663-689, April.
    3. Mortensen, Dale & Pissarides, Christopher, 2011. "Job Creation and Job Destruction in the Theory of Unemployment," Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 1, pages 1-19.
    4. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    5. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
    6. Gale, Douglas, 1987. "Limit theorems for markets with sequential bargaining," Journal of Economic Theory, Elsevier, vol. 43(1), pages 20-54, October.
    7. Takako Fujiwara-Greve & Masahiro Okuno-Fujiwara, 2009. "Voluntarily Separable Repeated Prisoner's Dilemma," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 993-1021.
    8. Gilboa, Itzhak & Matsui, Akihiko, 1992. "A model of random matching," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 185-197.
    9. Parikshit Ghosh & Debraj Ray, 1996. "Cooperation in Community Interaction Without Information Flows," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 491-519.
    10. Ken Burdett & Randall Wright, 1998. "Two-Sided Search with Nontransferable Utility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 1(1), pages 220-245, January.
    11. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    12. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-954, August.
    13. Rubinstein, Ariel & Wolinsky, Asher, 1985. "Equilibrium in a Market with Sequential Bargaining," Econometrica, Econometric Society, vol. 53(5), pages 1133-1150, September.
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    Citations

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    Cited by:

    1. Takako Fujiwara-Greve & Masahiro Okuno-Fujiwara & Nobue Suzuki, 2015. "Efficiency may improve when defectors exist," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 423-460, November.
    2. Duffie, Darrell & Qiao, Lei & Sun, Yeneng, 2018. "Dynamic directed random matching," Journal of Economic Theory, Elsevier, vol. 174(C), pages 124-183.

    More about this item

    Keywords

    Matching; Search; Undominated strategy equilibrium; Nash bargaining solution;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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