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arXiv · 1311.5728

The Prediction value

Maurice Koster·Sascha Kurz·Ines Lindner·Stefan Napel
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Abstract

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.

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Maurice Koster, Sascha Kurz, Ines Lindner, Stefan Napel. 2013-11-22. The Prediction value. https://doi.org/10.1007/s00355-016-1012-x

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