Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Cooperative Games (von Neumann–Morgenstern Stable Sets)

  • Ryo Kawasaki
  • Jun Wako
  • Shigeo Muto
Living reference work entry

Later version available View entry history

DOI: https://doi.org/10.1007/978-3-642-27737-5_99-2

Definition of the Subject

The von Neumann–Morgenstern stable set (hereafter stable set) is the first solution concept in cooperative game theory defined by J. von Neumann and O. Morgenstern. Though it was defined cooperative games in characteristic function form, von Neumann and Morgenstern gave a more general definition of a stable set in abstract games. Later, J. Greenberg and M. Chwe cleared a way to apply the stable set concept to the analysis of noncooperative games in strategic and extensive forms. Stable sets in a characteristic function form game may not exist, as was shown by W. F. Lucas for a ten-person game that does not admit a stable set. On the other hand, stable sets exist in many important games. In voting games, for example, stable sets exist, and they indicate what coalitions can be formed in detail. The core, on the other hand, can be empty in voting games, though it is one of the best known solution concepts in cooperative game theory. The analysis of stable sets is...


Coalition Structure Preference Profile Assignment Game External Stability Transferable Utility Game 
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Books and Reviews

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Graduate School of Decision Science and TechnologyTokyo Institute of TechnologyTokyoJapan
  2. 2.Department of EconomicsGakushuin UniversityTokyoJapan