Stable sets: a descriptive and comparative analysis
The notion of a stable set (introduced by von Neumann and Morgenstern, 1944) is an important tool in the field of Decision Theory. Since then, some alternative definitions have appeared in the literature: the admissible set (Kalai and Schmeidler, 1977), the generalized stable set (van Deemen, 1991), the M-stable set (Peris and Subiza, 2006), among others. Now, we are interested in obtaining the existence and the precise form of these stability notions, by according to the type of preference relation we have: total order, partial order, acyclic, tournament or weak-tournament.
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