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The bargaining set of four-person balanced games

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Abstract.

It is well known that in three-person transferable-utility cooperative games the bargaining set ℳi 1 and the core coincide for any coalition structure, provided the latter solution is not empty. In contrast, five-person totally-balanced games are discussed in the literature in which the bargaining set ℳi 1 (for the grand coalition) is larger then the core. This paper answers the equivalence question in the remaining four-person case. We prove that in any four-person game and for arbitrary coalition structure, whenever the core is not empty, it coincides with the bargaining set ℳi 1. Our discussion employs a generalization of balancedness to games with coalition structures.

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Received: August 2001/Revised version: April 2002

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Solymosi, T. The bargaining set of four-person balanced games. Game Theory 31, 1–11 (2002). https://doi.org/10.1007/s001820200102

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  • DOI: https://doi.org/10.1007/s001820200102

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