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M-stability: A reformulation of Von Neumann-Morgenstern stability

Author

Listed:
  • Peris, Josep E.

    (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)

  • Subiza, Begoña

    (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)

Abstract

The notion of a stable set (introduced by von Neumann and Morgenstern, 1944) is an important tool in the field of Decision Theory. However, unfortunately, the stable set has some disadvantages: it is not unique, it may select too many alternatives and, most importantly, it may fail to exist. Other stability notions have been introduced in the literature in order to solve the non-existence but, in some cases, they may fail to select "optimal outcomes", in the sense that they can select dominated alternatives although non dom-inated ones exist. We propose a new notion (M-stability) and compare it with previous proposals. Moreover, we analyze some properties (existence, uniqueness, optimality, unions and intersections, ...) of the different notions of stable set.

Suggested Citation

  • Peris, Josep E. & Subiza, Begoña, 2012. "M-stability: A reformulation of Von Neumann-Morgenstern stability," QM&ET Working Papers 12-4, University of Alicante, D. Quantitative Methods and Economic Theory.
    • Handle: RePEc:ris:qmetal:2012_004
    as

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    References listed on IDEAS

    as
    1. Peris, Josep E. & Subiza, Begona, 1994. "Maximal elements of not necessarily acyclic binary relations," Economics Letters, Elsevier, vol. 44(4), pages 385-388, April.
    2. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
    3. Robert Delver & Herman Monsuur, 2001. "Stable sets and standards of behaviour," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 555-570.
    4. Begoña Subiza & Josep Peris, 2005. "Strong maximals: Elements with maximal score in partial orders," Spanish Economic Review, Springer;Spanish Economic Association, vol. 7(2), pages 157-166, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    stable set; generalized-stable; socially-stable; m-stable; admissible set;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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