# 13-188/II (2013-11-25)

Author(s)
Maurice Koster, University of Amsterdam; Sascha Kurz, University of Bayreuth, Germany; Ines Lindner, VU University Amsterdam; Stefan Napel, University of Bayreuth, Germany
Keywords:
influence, voting games, cooperative games, Banzhaf value, Shapley value
JEL codes:
C71, D71, D72

We introduce the prediction value (PV) as a measure of players’ informational importance in probabilistic TU games. The latter combine a standard TU game and a probability distribution over the set of coalitions. Player i’s prediction value equals the difference between the conditional expectations of v(S) when i cooperates or not. We characterize the prediction value as a special member of the class of (extended) values which satisfy anonymity, linearity and a consistency property. Every n-player binomial semivalue coincides with the PV for a particular family of probability distributions over coalitions. The PV can thus be regarded as a power index in specific cases. Conversely, some semivalues – including the Banzhaf but not the Shapley value – can be interpreted in terms of informational importance.