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Rationality and Solutions to Nonconvex Bargaining Problems: Rationalizability and Nash Solutions

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  • Xu, Yongsheng
  • Yoshihara, Naoki
  • 吉原, 直毅

Abstract

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. 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 & 吉原, 直毅, 2012. "Rationality and Solutions to Nonconvex Bargaining Problems: Rationalizability and Nash Solutions," Discussion Paper Series 580, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:hituec:580
    Note: 41122
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    References listed on IDEAS

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    Cited by:

    1. Yongsheng Xu & Naoki Yoshihara, 2020. "Nonconvex Bargaining Problems: Some Recent Developments," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 7-41, November.
    2. Yongsheng Xu & Naoki Yoshihara, 2019. "An equitable Nash solution to nonconvex bargaining problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 769-779, September.
    3. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.

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    More about this item

    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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