Abstract
It is well-known that the core on several domains of cooperative transferable utility (TU) and nontransferable utility (NTU) games is characterized by various combinations of axioms containing some versions of the reduced game property, of its converse, or of the reconfirmation property with respect to the Davis–Maschler reduced game. We show that these characterizations are still valid for games with communication structures à la Myerson when using the notion of the reduced communication structure that establishes a new link between two inside players if they can communicate via outside players. Thus, it is shown that, if communication structures are present, the core may still be characterized on balanced TU games, on totally balanced TU games, on NTU games with a nonempty core, on the domains of all TU or NTU games, and on several other interesting domains of TU and NTU games. As a byproduct we construct, for any NTU game with communication structure, a certain classical NTU game with the same core that may be regarded as its Myerson restricted NTU game.
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Notes
Note that \(\nu (N,v,g)\) may not coincide with \(\nu (N,v/g)\) in general already for \(|N|=3\) as shown by an example Khmelnitskaya and Sudhölter (2013, p. 297), but using Kohlberg ’s (1971) characterization of the (pre)nucleolus by balanced collections of coalitions it may be deduced that \(\nu (N,v,g)=\nu (N,v/g)\) for all balanced (N, v, g).
When applied to sets, the “+” denotes the “Minkowski sum”, i.e., \(x+\mathbb R^S_+=\{x+y\mid y\in \mathbb R^S_+\}\).
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The authors are grateful to an anonymous referee and an associate editor of this journal for their detailed comments that helped to improve the writing of this paper. This research was supported by the Spanish Ministerio de Ciencia e Innovación under project ECO2012-33618, co-funded by the ERDF. Moreover, the first author was supported by the Basque Country University (UFI11/51 and GIU13/31), and the second author was supported by The Danish Council for Independent Research|Social Sciences under the FINQ project (Grant ID: DFF-1327-00097).
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Albizuri, M.J., Sudhölter, P. Characterizations of the core of TU and NTU games with communication structures. Soc Choice Welf 46, 451–475 (2016). https://doi.org/10.1007/s00355-015-0924-1
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DOI: https://doi.org/10.1007/s00355-015-0924-1