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The Banzhaf value in the presence of externalities
Álvarez-Mozos, Mikel; Tejada, Oriol
Universitat de Barcelona
We propose two generalizations of the Banzhaf value for partition function form games. In both cases our approach is based on probability distributions over the set of coalition structures that may arise for any given set of players. First, we introduce a family of values, one for each collection of these latter probability distributions, defined as the Banzhaf value of a coalitional game obtained as the expectation taken according to the given probability distributions of the original partition function form game. For each value of the family we provide two characterization results within the set of all partition function form games. Both results rely on a property of neutrality with respect to the amalgamation of players. Second, we propose another family of values that differ from the previous ones in that the latter values take into account only the information about the most likely coalition structure that may arise according to the given probability distributions. Each value of the second family is also characterized in two results by means of a collusion neutrality property. Unlike the characterizations of the first approach, these characterizations can be restricted to the set of simple games in partition function form.
Teoria de jocs
Teoria de l'estimació
Jocs cooperatius (Matemàtica)
Presa de decisions (Estadística)
Ciències socials
Game theory
Estimation theory
Cooperative games (Mathematics)
Statistical decision
Social sciences
(c) Springer Verlag, 2014
Springer Verlag

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