Abstract
This article characterises stable sets in an abstract game. We show that every stable subset of the pure strategies for the game is characterised as a fixed point of the mapping assigning to each upper boundedly preordered subset of the strategies the set of all its maximal elements.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dugunji, J. : Topology. xvi+447, pp. Wm. C. Brown Publishers, Iowa, USA (1966)
Jiang, D.: Realizability of of Expected Equilibria of N-Person Condition Game under Strong Knowledge System. International Journal of Innovative Computing, Information and Control 2(4), 761–770 (2006)
Jiang, D.: N-M Stable Set of a Regular Game and its Unique Existence Theorem in System ZFC. Journal of Systems Science and Mathematical Sciences (to appear, 2010)
Lucas, W.F.: Von Neumann-Morgenstern Stable Sets. In: Aumann, R.J., Hart, S. (eds.) Handbook of Game Theory, vol. I, ch. 17, pp. 543–590. Elsevier Science Publisher B.V., Amsterdam (1992)
von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944); 2’nd edition (1947); 3’rd edition (1953)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Matsuhisa, T. (2010). A Characterisation of Stable Sets in Games with Transitive Preference. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17458-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-17458-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17457-5
Online ISBN: 978-3-642-17458-2
eBook Packages: Computer ScienceComputer Science (R0)