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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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    1. Alvin E. Roth, 1977. "Individual Rationality and Nash's Solution to the Bargaining Problem," Mathematics of Operations Research, INFORMS, vol. 2(1), pages 64-65, February.
    2. Marco Mariotti, 1999. "Fair Bargains: Distributive Justice and Nash Bargaining Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 733-741.
    3. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
    4. Bossert, Walter, 1994. "Rational choice and two-person bargaining solutions," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 549-563, November.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. Thomson, William, 1981. "A class of solutions to bargaining problems," Journal of Economic Theory, Elsevier, vol. 25(3), pages 431-441, December.
    7. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    8. Peters, H.J.M. & Vermeulen, A.J., 2006. "WPO, COV and IIA bargaining solutions," Research Memorandum 021, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(3), pages 307-317.
    10. 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.
    11. Michele Lombardi & Marco Mariotti, 2009. "Uncovered bargaining solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 601-610, November.
    12. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
    13. 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.
    14. Mariotti, Marco, 1998. "Extending Nash's Axioms to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 22(2), pages 377-383, February.
    15. Yongsheng Xu, 2002. "Functioning, capability and the standard of living - an axiomatic approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 387-399.
    16. John A. Weymark & Kai-yuen Tsui, 1997. "Social welfare orderings for ratio-scale measurable utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 241-256.
    17. 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.
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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. 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.
    3. 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.

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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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