Abstract
This paper introduces yet another algorithm to compute the nucleolus of a standard tree game. One advantage of this algorithm is that it provides a very intuitive interpretation of the nucleolus, under which the players participate in a joint enterprize in which each group sends a member to help the community. Another advantage is that it demonstrates monotonicity properties of the nucleolus within this class of games. As a consequence the nucleolus of a tree game can be extended to a population monotonic allocation scheme.
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This article is dedicated to the memory of Michael. This paper is a result of a longstanding working together. We had long breaks and short, but intensive periods of interaction, the final one only three weeks before his passing away.
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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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Maschler, M., Potters, J. & Reijnierse, H. The nucleolus of a standard tree game revisited: a study of its monotonicity and computational properties. Int J Game Theory 39, 89–104 (2010). https://doi.org/10.1007/s00182-009-0176-3
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DOI: https://doi.org/10.1007/s00182-009-0176-3