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

Josep E. Peris and Begoña Subiza

No 12-4, QM&ET Working Papers from University of Alicante, D. Quantitative Methods and Economic Theory

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.

Keywords: stable set; generalized-stable; socially-stable; m-stable; admissible set (search for similar items in EconPapers)
JEL-codes: D11 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2012-03-07
New Economics Papers: this item is included in nep-gth and nep-mic
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Persistent link: https://EconPapers.repec.org/RePEc:ris:qmetal:2012_004

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