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Revealed group preferences on non-convex choice problems

Author

Listed:
  • Efe A. Ok

    (Department of Economics, New York University, 269 Mercer St., New York, NY 10003, USA)

  • Lin Zhou

    (Department of Economics, Duke University, Durham, NC 27708, USA)

Abstract

This paper studies the conditions under which the basic results of the revealed preference theory can be established on the domain of choice problems which include non-convex feasible sets; the exercise is closely related to the works of Peters and Wakker (1991) and Bossert (1994). We show that while no continuous choice function can satisfy strong Pareto optimality over the class of all compact and comprehensive choice problems, strong Pareto optimality, Arrow's choice axiom, upper hemicontinuity and a weak compromisation postulate turn out to be necessary and sufficient to represent choice correspondences by continuous, strictly increasing and quasiconcave real-valued functions. Some applications of our main findings to axiomatic bargaining theory are also studied.

Suggested Citation

  • Efe A. Ok & Lin Zhou, 1999. "Revealed group preferences on non-convex choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 671-687.
    • Handle: RePEc:spr:joecth:v:13:y:1999:i:3:p:671-687
    Note: Received: December 2, 1996; revised version: February 27, 1998
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    Citations

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    Cited by:

    1. M. Hinojosa & A. Mármol & J. Zarzuelo, 2008. "Inequality averse multi-utilitarian bargaining solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 597-618, December.
    2. Ok, Efe A. & Zhou, Lin, 2000. "The Choquet Bargaining Solutions," Games and Economic Behavior, Elsevier, vol. 33(2), pages 249-264, November.
    3. Hiroki Nishimura & Efe A. Ok & John K.-H. Quah, 2017. "A Comprehensive Approach to Revealed Preference Theory," American Economic Review, American Economic Association, vol. 107(4), pages 1239-1263, April.
    4. Stan Cheung & Marco Mariotti & Roberto Veneziani, 2024. "The Hard Problem and the Tyranny of the Loser," Working Papers 971, Queen Mary University of London, School of Economics and Finance.
    5. John Quah & Hiroki Nishimura & Efe A. Ok, 2013. "A Unified Approach to Revealed Preference Theory: The Case of Rational Choice," Economics Series Working Papers 686, University of Oxford, Department of Economics.
    6. Ok, Efe A., 1998. "Inequality averse collective choice," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 301-321, October.
    7. Miguel Ángel Hinojosa & Amparo Mª Mármol & José Manuel Zarzuelo, 2007. "Multi-Utilitarian Bargaining Solutions," Working Papers 07.13, Universidad Pablo de Olavide, Department of Economics.
    8. Nishimura, Hiroki & Ok, Efe A., 2014. "Non-existence of continuous choice functions," Journal of Economic Theory, Elsevier, vol. 153(C), pages 376-391.

    More about this item

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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