Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Cooperative Games (von Neumann–Morgenstern Stable Sets)

Living reference work entry
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...

Keywords

Coalition Structure Preference Profile Assignment Game External Stability Transferable Utility Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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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