Abstract
A core concept is a solution concept on the class of balanced games that exclusively selects core allocations. We show that every continuous core concept that satisfies both the equal treatment property and a new property called independence of irrelevant core allocations (IIC) necessarily selects egalitarian allocations. IIC requires that, if the core concept selects a certain core allocation for a given game, and this allocation is still a core allocation for a new game with a core that is contained in the core of the first game, then the core concept also chooses this allocation as the solution to the new game. When we replace the continuity requirement by a weak version of additivity we obtain an axiomatization of the egalitarian solution concept that assigns to each balanced game the core allocation minimizing the Euclidean distance to the equal share allocation.
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Javier Arin gratefully acknowledges the financial support by EHU, project nr, UPV 035.321-HB048/97 and by the Spanish Ministry of Education and Science, project nr, SEJ2006-05455.
Jeroen Kuipers gratefully acknowledges the financial support by the Basque Government, Department of Research and Education.
Dries Vermeulen gratefully acknowledges the financial support of the Dutch Organization for Scientific Research NWO.
We thank two referees, an associate editor and Peter Sudhölter for their remarks that helped to improve the presentation of this article considerably.
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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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Arin, J., Kuipers, J. & Vermeulen, D. An axiomatic approach to egalitarianism in TU-games. Int J Game Theory 37, 565–580 (2008). https://doi.org/10.1007/s00182-008-0133-6
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DOI: https://doi.org/10.1007/s00182-008-0133-6