Games and Capacities on Partitions
نویسنده
چکیده
We consider capacities and games whose value v(S) depend on the organization of N \ S, this organization being represented by a partition. Hence we deal with capacities and games depending on two arguments: a subset (coalition) S and a partition π containing S. We call embedded coalition any such pair (S, π). We first provide a suitable structure for the set of embedded coalitions, study its properties, and find the Möbius function for this structure. Then, we define games and capacities on this structure and study their properties. We propose also a concept similar to the Shapley value, and provide an axiomatization of it. Lastly, we give some insights on the Choquet integral. Keywords— capacity, fuzzy measure, partition, Möbius transform, Shapley value
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