Abstract
In this paper we consider coalition configurations (Albizuri et al. in Games Econ Behav 57:1–17, 2006), that is, families of coalitions not necessarily disjoint whose union is the grand coalition, and give a generalization of the Shapley value (Contributions to the theory of games II, Princeton University Press, Princeton, pp 307–317, 1953) and the Owen value (Essays in mathematical economics and game theory, Springer, Berlin, pp 76–88, 1977) when coalition configurations form. This will be an alternative definition to the one given by Albizuri et al.
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Notes
This solution concept is defined, following Levy and McLean (1989), for a fixed coalition structure. Our solution, presented in the next section, is more general and it does not depend on any particular coalition configuration.
We denote by \({\mathbb {R}}_{+}^{N}\) the set of \(\vert N\vert \) -tuples with strictly positive components indexed by the elements in \(N\).
Stationary subgame perfect equilibrium.
See Theorem 5.1 in Albizuri et al. (2006) for Efficiency, Linearity and Intercoalitional Symmetry (called Coalitional Symmetry). Coalition Configuration Positivity, Intracoalitional Parnership, Null Players Out and Merger follow easily from the definition.
References
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This paper has benefit from the comments of two anonymous referees. Usual disclaimer applies.
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This research has been partially supported by the Ministerio de Ciencia e Innovación (projects ECO2011-23460 and ECO2012-33618), Xunta de Galicia (project 10PXIB362299PR) and the University of the Basque Country (GIU 13/31 and UFI11/5).
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Albizuri, M.J., Vidal-Puga, J. Values and coalition configurations. Math Meth Oper Res 81, 3–26 (2015). https://doi.org/10.1007/s00186-014-0484-7
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DOI: https://doi.org/10.1007/s00186-014-0484-7