The consistent Shapley value for hyperplane games
International Journal of Game Theory
A lexicographical solution concept in an n-person cooperative fuzzy game
Fuzzy Sets and Systems
Fuzzy Sets and Systems - Theme: Decision and optimization
Fuzzy and Multiobjective Games for Conflict Resolution (Studies in Fuzziness and Soft Computing)
Fuzzy and Multiobjective Games for Conflict Resolution (Studies in Fuzziness and Soft Computing)
Fuzzy games: A characterization of the core
Fuzzy Sets and Systems
Max-consistency, complement-consistency and the core of fuzzy games
Fuzzy Sets and Systems
The robustness of generalized abstract fuzzy economies in generalized convex spaces
Fuzzy Sets and Systems
The equal allocation of nonseparable costs: An extension under fuzzy behavior
Fuzzy Sets and Systems
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In the framework of fuzzy games, we offer an extension of the reduced game introduced by Hart and Mas-Colell, which we name the self-reduced game. According to consistency which related to the self-reduced game, we provide a definition of the consistent value which is a generalization of the Shapley value of fuzzy games. We adopt three existing concepts from coalitional game theory and reinterpret them in the framework of fuzzy games. The first one is that there exists a unique potential function and the resulting payoff vector coincides with the consistent value. Second, based on the properties of balanced contributions and consistency, we offer several axiomatizations of the consistent value. Finally, we propose a dynamic process to illustrate that the consistent value can be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments.