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Bounds for the Nakamura number

Author

Listed:
  • Josep Freixas

    (Universitat Politècnica de Catalunya)

  • Sascha Kurz

    (University of Bayreuth)

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.

Suggested Citation

  • Josep Freixas & Sascha Kurz, 2019. "Bounds for the Nakamura number," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 607-634, April.
    • Handle: RePEc:spr:sochwe:v:52:y:2019:i:4:d:10.1007_s00355-018-1164-y
    DOI: 10.1007/s00355-018-1164-y
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    References listed on IDEAS

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