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

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  • 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.

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Bibliographic Info

Paper provided by Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica in its series QM&ET Working Papers with number 12-4.

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Length: 23 pages
Date of creation: 07 Mar 2012
Date of revision:
Handle: RePEc:ris:qmetal:2012_004

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Keywords: stable set; generalized-stable; socially-stable; m-stable; admissible set;

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  1. Josep Enric Peris Ferrando & Begoña Subiza Martínez, 1992. "Maximal elements of non necessarily acyclic binary relations," Working Papers. Serie AD 1992-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Begoña Subiza & Josep Peris, 2005. "Strong maximals: Elements with maximal score in partial orders," Spanish Economic Review, Springer, vol. 7(2), pages 157-166, 06.
  3. Robert Delver & Herman Monsuur, 2001. "Stable sets and standards of behaviour," Social Choice and Welfare, Springer, vol. 18(3), pages 555-570.
  4. E. Kalai & D. Schmeidler, 1975. "An Admissible Set Occurring in Various Bargaining Situations," Discussion Papers 191, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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