Games with Fuzzy Coalitions
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In this chapter the set X is interpreted as a set of players who participate in interactive activities by forming fuzzy coalitions,i.e., coalitions which they may belong to in various degrees. Such a coalition will be represented by a fuzzy subset of X. If A is a fuzzy subset of X representing a fuzzy coalition, then we interprete the membership degree of a player x ∈ X to A as the share of the individual worth of the player x which is invested as his participation in the fuzzy coalition A. In a specific social environment the class of fuzzy coalitions which can be effectively constituted by the players is determined by exogeneous rules. We always assume that this class is a T ∞ -tribe.ℐ which is given a priori, and the term fuzzy coalition is used to determine an element of.ℐ. A game on.ℐ or, simply, a game is a function v: ℐ → ℝ with v(Ø) = 0. The class of all games on ℐ is denoted GAMES ℐ or, simply, GAMES,when there is no possibility of confusion. GAMES ℐ,is an algebra with the operations naturally induced from ℝ.
KeywordsAdditive Function Linear Subspace Bounded Variation Fuzzy Subset Market Game
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