A characterization result on the coincidence of the prenucleolus and the Shapley value. (English) Zbl 1188.91027
Basu, Banasri (ed.) et al., Econophysics & economics of games, social choices and quantitative techniques. Some papers are the proceedings of the econophys-Kolkata IV workshop, Kolkata, India, march 9–13, 2009. Milano: Springer (ISBN 978-88-470-1500-5/hbk). New Economic Windows, 362-371 (2010).
Summary: A \(PS\) game is a TU game where the sum of a player’s marginal contribution to any coalition and its complement coalition is a player specific constant. For \(PS\) games the prenucleolus coincides with the Shapley value. In this short paper we show that if \({\mathcal L}\) is an anonymous linear subspace of TU games such that it has a basis which is a subset of the class of unanimity games, then the prenucleolus coincides with the Shapley value on \({\mathcal L}\) if and only if \({\mathcal L}\) is a subset of the class of all \(PS\) games.
For the entire collection see [Zbl 1178.91006].
For the entire collection see [Zbl 1178.91006].
MSC:
| 91A12 | Cooperative games |
