Abstract
A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson value for games with limited communication.
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We thank two referees for their useful comments. This research was partly carried out while the second author was visiting the Tinbergen Institute, VU University Amsterdam, on NWO-Grant 047.017.017 within the framework of Dutch–Russian cooperation. This author was also financially supported by the RFBR Grant 09-06-00155.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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van den Brink, R., Katsev, I. & van der Laan, G. Axiomatizations of two types of Shapley values for games on union closed systems. Econ Theory 47, 175–188 (2011). https://doi.org/10.1007/s00199-010-0530-5
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DOI: https://doi.org/10.1007/s00199-010-0530-5