Cooperation tendencies and evaluation of games

Abstract

Multinomial probabilistic values were first introduced by one of us in reliability and later on by the other, independently, as power indices. Here we study them on cooperative games from several viewpoints, and especially as a powerful generalization of binomial semivalues. We establish a dimensional comparison between multinomial values and binomial semivalues and provide two characterizations within the class of probabilistic values: one for each multinomial value and another for the whole family. An example illustrates their use in practice as power indices.