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Rationality and Solutions to Nonconvex Bargaining Problems: Rationalizable, Asymmetric and Nash Solutions


  • Xu, Yongsheng
  • Yoshihara, Naoki


Conditions α and β are two well-known rationality conditions in the theory of rational choice. This paper examines the implications of weaker versions of these two rationality conditions in the context of solutions to nonconvex bargaining problems. It is shown that, together with the standard axioms of efficiency and strict individual rationality, they imply rationalizability of solutions to nonconvex bargaining problems. We then characterize asymmetric Nash solutions by imposing a continuity and the scale invariance requirements. We also give a characterization of the Nash solution by using the two rationality conditions. These results make a further connection between solutions to non-convex bargaining problems and rationalizability of choice function in the theory of rational choice.

Suggested Citation

  • Xu, Yongsheng & Yoshihara, Naoki, 2011. "Rationality and Solutions to Nonconvex Bargaining Problems: Rationalizable, Asymmetric and Nash Solutions," Discussion Paper Series 551, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hit:hituec:551
    Note: This Version: April 2011

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    References listed on IDEAS

    1. Kurz,Heinz D. & Salvadori,Neri, 1997. "Theory of Production," Cambridge Books, Cambridge University Press, number 9780521588676, March.
    2. Takao Fujimoto & Arrigo Opocher, 2010. "Commodity Content In A General Input-Output Model," Metroeconomica, Wiley Blackwell, vol. 61(3), pages 442-453, July.
    3. Naoki Yoshihara & Roberto Veneziani, 2010. "Commodity Content In A General Input-Output Model: A Comment," Metroeconomica, Wiley Blackwell, vol. 61(4), pages 740-748, November.
    4. Takao Fujimoto & Yukihiko Fujita, 2008. "A Refutation Of The Commodity Exploitation Theorem," Metroeconomica, Wiley Blackwell, vol. 59(3), pages 530-540, July.
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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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