A reformulation of von Neumann–Morgenstern stability: m-stability

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Title: A reformulation of von Neumann–Morgenstern stability: m-stability
Authors: Peris, Josep E. | Subiza, Begoña
Research Group/s: Métodos Cuantitativos para la Economía
Center, Department or Service: Universidad de Alicante. Departamento de Métodos Cuantitativos y Teoría Económica
Keywords: Stable set | Decision Theory | m-stability
Knowledge Area: Fundamentos del Análisis Económico
Issue Date: Jul-2013
Publisher: Elsevier
Citation: Mathematical Social Sciences. 2013, 66(1): 51-55. doi:10.1016/j.mathsocsci.2013.01.001
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, stable sets may fail to exist. Other stability notions have been introduced in the literature in order to solve the non-existence problem. We propose a new notion, that we call m-stability, and compare it with previous proposals. Moreover, we analyze some properties (existence, uniqueness, unions and intersections, …) of the different notions of a stable set. Finally, we use the Shapley–Scarf market model with indivisible goods in order to show that the non-empty core is an mm-stable set, and does not fulfill, in general, the other stability notions.
URI: http://hdl.handle.net/10045/44552
ISSN: 0165-4896 (Print) | 1879-3118 (Online)
DOI: 10.1016/j.mathsocsci.2013.01.001
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version: http://dx.doi.org/10.1016/j.mathsocsci.2013.01.001
Appears in Collections:INV - DMCTE - Artículos de Revistas

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