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This is a post-peer-review, pre-copyedit version of an article published in Social choice and welfare. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00355-018-1164-y., 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. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature., Peer Reviewed, Postprint (author's final draft)

This paper considers the computational complexity of the design of voting rules, which is formulated by simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.

This paper considers the computational complexity of the design of voting rules, which is formulated by simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.

This paper considers the computational complexity of the design of voting rules, which is formulated by simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.

ISER discussion paper, March 2006 Revised July 2006 (Originally entitled "Computational Complexity in the Design of Voting Systems."), This paper discusses an aspect of computational complexity in social choice theory. We consider the problem of designing voting rules, which is formulated in terms of simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.

ISER discussion paper, March 2006 Revised July 2006 (Originally entitled "Computational Complexity in the Design of Voting Systems."), This paper discusses an aspect of computational complexity in social choice theory. We consider the problem of designing voting rules, which is formulated in terms of simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.