Bounds for the Nakamura number

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Freixas, Josep ; Kurz, Sascha:
Bounds for the Nakamura number.
In: Social Choice and Welfare. Bd. 52 (2019) Heft 4 . - S. 607-634.
ISSN 1432-217X
DOI: https://doi.org/10.1007/s00355-018-1164-y

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Abstract

The Nakamura number is an appropriate invariant of a simple game in order to study the existence of social equilibria and the possibility of cycles. For symmetric quota games its number can be obtained by an easy formula. For some subclasses of simple games the corresponding Nakamura number has also been characterized. However, in general, not much is known about lower and upper bounds depending of invariants of simple, complete or weighted games. Here, we present several results in that direction.