Axiomatic of the Shapley value of a game with a priori unions
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In this paper, we define a modification of the Shapley value for the model of TU games with a priori unions. We provide two characterizations of this value and a new characterization of the Banzhaf–Owen coalitional value.
KeywordsCooperative game Shapley value A priori unions Coalitional value
Mathematics Subject Classification (2010)91A12
Financial support from Ministerio de Ciencia y Tecnología and FEDER through grants MTM2011-27731-C03-02 and ECO2011-23460 is gratefully acknowledged. The authors are also very grateful for the interesting suggestions given by three anonymous referees.
- Banzhaf JF (1965) Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Rev 19:317–343 Google Scholar
- Kamijo Y (2013) The collective value: a new solution for games with coalition structures. Top. Article in press. doi: 10.1007/s11750-011-0191-y
- Meng FY (2011) The Banzhaf–Owen value for fuzzy games with a coalition structure. Eng Technol 80:855–859 Google Scholar
- Owen G (1982) Modification of the Banzhaf–Coleman index for games with a priori unions. In: Holler MJ (ed) Power, voting and voting power. Physica-Verlag, Würzburg, pp 232–238 Google Scholar
- Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307–317 Google Scholar