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Nash bargaining for log-convex problems

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  • Qin, CZ
  • Shi, S
  • Tan, G

Abstract

We introduce log-convexity for bargaining problems. With the requirement of some basic regularity conditions, log-convexity is shown to be necessary and sufficient for Nash’s axioms to determine a unique single-valued bargaining solution up to choices of bargaining powers. Specifically, we show that the single-valued (asymmetric) Nash solution is the unique solution under Nash’s axioms without that of symmetry on the class of regular and log-convex bargaining problems, but this is not true on any larger class. We apply our results to bargaining problems arising from duopoly and the theory of the firm. These problems turn out to be log-convex but not convex under familiar conditions. We compare the Nash solution for log-convex bargaining problems with some of its extensions in the literature.

Suggested Citation

  • Qin, CZ & Shi, S & Tan, G, 2015. "Nash bargaining for log-convex problems," University of California at Santa Barbara, Recent Works in Economics qt5dn8c7hp, Department of Economics, UC Santa Barbara.
  • Handle: RePEc:cdl:ucsbrw:qt5dn8c7hp
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    1. Hans Peters & Dries Vermeulen, 2012. "WPO, COV and IIA bargaining solutions for non-convex bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 851-884, November.
    2. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716.
    3. Schmalensee, Richard, 1987. "Competitive advantage and collusive optima," International Journal of Industrial Organization, Elsevier, vol. 5(4), pages 351-367.
    4. Masahiko Aoki, 2013. "A Model of the Firm as a Stockholder-Employee Cooperative Game," Chapters, in: Comparative Institutional Analysis, chapter 9, pages 141-142, Edward Elgar Publishing.
    5. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    6. Ross, Stephen A, 1973. "The Economic Theory of Agency: The Principal's Problem," American Economic Review, American Economic Association, vol. 63(2), pages 134-139, May.
    7. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    8. Binmore, Ken, 2007. "Playing for Real: A Text on Game Theory," OUP Catalogue, Oxford University Press, number 9780195300574.
    9. Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
    10. Marco Mariotti, 1998. "Nash bargaining theory when the number of alternatives can be finite," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 413-421.
    11. Xu, Yongsheng & Yoshihara, Naoki, 2006. "Alternative characterizations of three bargaining solutions for nonconvex problems," Games and Economic Behavior, Elsevier, vol. 57(1), pages 86-92, October.
    12. Mariotti, Marco, 1998. "Extending Nash's Axioms to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 22(2), pages 377-383, February.
    13. Jens Leth Hougaard & Mich Tvede, 2003. "Nonconvex n-person bargaining: efficient maxmin solutions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(1), pages 81-95, January.
    14. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
    15. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    16. Qin, Cheng-Zhong & Tan, Guofu & Wong, Adam Chi Leung, 2019. "Implementation of Nash bargaining solutions with non-convexity," Economics Letters, Elsevier, vol. 178(C), pages 46-49.
    17. Conley, John P. & Wilkie, Simon, 1996. "An Extension of the Nash Bargaining Solution to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 13(1), pages 26-38, March.
    18. Miyazaki, Hajime, 1984. "Internal Bargaining, Labor Contracts, and a Marshallian Theory of the Firm," American Economic Review, American Economic Association, vol. 74(3), pages 381-393, June.
    19. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
    20. Vincenzo Denicolò & Marco Mariotti, 2000. "Nash Bargaining Theory, Nonconvex Problems and Social Welfare Orderings," Theory and Decision, Springer, vol. 48(4), pages 351-358, June.
    21. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    22. McDonald, Ian M & Solow, Robert M, 1981. "Wage Bargaining and Employment," American Economic Review, American Economic Association, vol. 71(5), pages 896-908, December.
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    1. Carlos Alós-Ferrer & Jaume García-Segarra & Miguel Ginés-Vilar, 2018. "Anchoring on Utopia: a generalization of the Kalai–Smorodinsky solution," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(2), pages 141-155, October.
    2. P. Jean-Jacques Herings & A. Predtetchinski, 2016. "Bargaining under monotonicity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 221-243, June.

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    More about this item

    Keywords

    Economic Theory; Econometrics; Applied Economics;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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