Abstract.
Consider a special stable partition problem in which the player's preferences over sets to which she could belong are identical with her preferences over the most attractive member of a set and in case of indifference the set of smaller cardinality is preferred. If the preferences of all players over other (individual) players are strict, a strongly stable and a stable partition always exists. However, if ties are present, we show that both the existence problems are NP-complete. These results are very similar to what is known for the stable roommates problem.
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Received: July 2000/Revised: October 2002
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ID="*" This work was supported by the Slovak Agency for Science, contract #1/7465/20 “Combinatorial Structures and Complexity of Algorithms”.
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Cechlárová, K., Hajduková, J. Computational complexity of stable partitions with B-preferences. Game Theory 31, 353–364 (2003). https://doi.org/10.1007/s001820200124
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DOI: https://doi.org/10.1007/s001820200124