The Banzhaf Value in the Presence of Externalities
UB Economics Working Papers E14/302
20 Pages Posted: 27 Feb 2014 Last revised: 3 Mar 2014
Date Written: January 16, 2014
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 possible coalition structures that may arise for any given set of agents. First, we introduce a family of values, one for each collection of the latter probability distributions, defined as the Banzhaf value of an expected coalitional game. Then, we provide two characterization results for this new family of values within the framework of all partit ion function games. Both results rely on a property of neutrality with respect to am algamation of players. Second, as this collusion transformation fails to be meaningful for simple games in partition function form, we propose another generalization of the Banzhaf value which also builds on probability distributions of the above type. This latter family is characterized by means of a neutrality property which uses an amalgamation transformation of players for which simple games are closed.
Keywords: Banzhaf value, Externalities, Games in pa rtition function form, Simple games
JEL Classification: C71
Suggested Citation: Suggested Citation