The bargaining set of four-person balanced games |
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Authors: | Tamás Solymosi |
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Institution: | (1) Department of Operations Research, Budapest University of Economic Sciences and Public Administration, 1828 Budapest, Pf. 489, Hungary, phone: +36-1-456 6757, fax: +36-1-456 6435, e-mail: tamas.solymosi@opkut.bke.hu, HU |
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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.
Received: August 2001/Revised version: April 2002 |
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Keywords: | : cooperative game bargaining set core coalition structure |
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