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Keywords:
coalitional games; non-transferable utility; fuzzy quantity; fuzzy cooperative game; core of a game; superadditivity
coalitional games; non-transferable utility; fuzzy quantity; fuzzy cooperative game; core of a game; superadditivity
Summary:
One of the possible models of fuzzification of non-transferable utility (NTU) coalitional games was extensively treated in [4]. In this paper, we suggest an alternative structure of fuzzification of the NTU games, where for every coalition a fuzzy class of (generally crisp) sets of its admissible pay-off vectors is considered. It is shown that this model of a fuzzy coalitional game can be represented by a fuzzy class of deterministic NTU games, and its basic concepts like the superadditivity or the core can be transparently introduced by means of that class of games.
References:
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[4] Mareš M.: Fuzzy Cooperative Games. Cooperation with Vague Expectations. Physica–Verlag, Heidelberg 2002 MR 1841340 | Zbl 1037.91007
[5] Mareš M., Vlach M.: Concept of linear coalition game. Tatra Mountains Math. Publications (to appear)
[6] Mareš M., Vlach M.: Linear coalitional games and their fuzzy extensions. Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems (to appear) MR 1843262 | Zbl 1113.91303
[7] Rosenmüller J.: The Theory of Games and Markets. North–Holland, Amsterdam 1982 Zbl 0464.90089
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