The Prediction Value

Tinbergen Institute Discussion Paper 13-188/II

28 Pages Posted: 30 Nov 2013

See all articles by Maurice Koster

Maurice Koster

Amsterdam School of Economics, University of Amsterdam

Sascha Kurz

University of Bayreuth

Ines Lindner

Free University Amsterdam

Stefan Napel

University of Bayreuth

Date Written: November 29, 2013

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.

Keywords: influence, voting games, cooperative games, Banzhaf value, Shapley value

JEL Classification: C71, D71, D72

Suggested Citation

Koster, Maurice and Kurz, Sascha and Lindner, Ines and Napel, Stefan, The Prediction Value (November 29, 2013). Tinbergen Institute Discussion Paper 13-188/II, Available at SSRN: https://ssrn.com/abstract=2361444 or http://dx.doi.org/10.2139/ssrn.2361444

Maurice Koster (Contact Author)

Amsterdam School of Economics, University of Amsterdam ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands
+31 205254226 (Phone)

HOME PAGE: http://www.uva.nl/profiel/k/o/m.a.l.koster/m.a.l.koster.html

Sascha Kurz

University of Bayreuth ( email )

Universitätsstr. 30
Lehrstuhl für Wirtschaftsmathematik
Bayreuth, Bavaria D-95440
Germany
+49 921 55 7353 (Phone)
+49 921 55 7352 (Fax)

HOME PAGE: http://www.wm.uni-bayreuth.de/index.php?id=sascha

Ines Lindner

Free University Amsterdam ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

Stefan Napel

University of Bayreuth ( email )

Universitatsstr 30
Bayreuth, D-95447
Germany

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