Subjective evaluations of n-person games
Using an axiomatization of subjective expected utility due to Fishburn, we characterize a class of utility functions over a set of n-person games in characteristic-function form. A probabilistic value is defined as the expectation of some player's marginal contribution with respect to some probability measure on the set of coalitions of other players. We decribe conditions under which a utility function on the set of n-person games is a probabilistic value; we prove as well an analogous result for simple games. We present additional axioms that characterize the semivalues and, in turn, the Shapley and Banzhaf values.