Koster, Maurice Kurz, Sascha Lindner, Ines Napel, Stefan
Year of Publication:
Tinbergen Institute Discussion Paper 13-188/II
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 is 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.
influence voting games cooperative games Banzhaf value Shapley value