## Abstract

The Nakamura number is an appropriate invariant of a simple game 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 on invariants of simple, complete or weighted games. Here, we survey such results and highlight connections with other game theoretic concepts.

## Keywords

Nakamura number Stability Simple games Complete simple games Weighted games Bounds## Mathematics Subject Classification

91A12 91B14 91B12## Notes

### Acknowledgements

The authors thank the anonymous referees and the associate editor for their careful reading of a preliminary version of this paper. Their constructive remarks were extremely useful to improve its presentation.

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