Social Choice and Welfare

, Volume 52, Issue 4, pp 607–634 | Cite as

Bounds for the Nakamura number

  • Josep Freixas
  • Sascha KurzEmail author
Original Paper


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.


Nakamura number Stability Simple games Complete simple games Weighted games Bounds 

Mathematics Subject Classification

91A12 91B14 91B12 



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Engineering, School of ManresaUniversitat Politècnica de CatalunyaCataloniaSpain
  2. 2.Department of Mathematics, Physics, and Computer ScienceUniversity of BayreuthBayreuthGermany

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