Abstract
This article characterises stable sets in preordered sets. We show that every stable subset of a preordered set is characterised as a fixed point of the mapping assigning the set of all its maximal elements to each upper bounded subset of the preordered set. This result gives a characterisation of stable sets in strategic games with transitive preferences.
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Dedicated Shoji Koizumi on the occasion of his “Béi-Ju”.
The “Béi-Ju” is the Japanese celebratory word for his/her “Eighty-eighth birthday”.
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Matsuhisa, T. A characterisation of stable sets in preordered structure. 4OR-Q J Oper Res 10, 33–41 (2012). https://doi.org/10.1007/s10288-011-0171-y
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DOI: https://doi.org/10.1007/s10288-011-0171-y