Abstract
A communication process in the S5-knowledge model is presented which leads to a Nash equilibrium of a strategic form game through robust messages. In the communication process each player predicts the other players’ actions under his/her private information. The players communicate privately their conjectures through message according to the communication graph, where each recipient of the message learns and revises his/her conjecture. The emphasis is on that each player sends not exact information about his/her individual conjecture but robust information about the conjectures to an accuracy ε.
AMS 2000 Mathematics Subject Classification: Primary 91A35, Secondary 03B45.
Journal of Economic Literature Classification: C62, C78.
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
Aumann, R.J., Brandenburger, A.: Epistemic conditions for mixed strategy Nash equilibrium. Econometrica 63, 1161–1180 (1995)
Bacharach, M.: Some extensions of a claim of Aumann in an axiomatic model of knowledge. Journal of Economic Theory 37, 167–190 (1985)
Binmore, K.: Fun and Games. xxx+, p. 642 Lexington, Massachusetts USA: D. C. Heath and Company (1992).
Jordan, J.S.: Bayesian learning in normal form games. Games and Economic Behavior 3, 60–81 (1991)
Kalai, E., Lehrer, E.: Rational learning to mixed strategy Nash equilibrium. Econometrica 61, 1019–1045 (1993)
Matsuhisa, T.: Communication leading to mixed strategy Nash equilibrium I. In: Maruyama, T. (ed.) Mathematical Economics, Suri-Kaiseki-Kenkyusyo Kokyuroku, vol. 1165, pp. 245–256 (2000)
Matsuhisa, T.: Communication leading to epsilon-mixed strategy Nash equilibrium, Working paper. IMGTA XIV. The extended abstract was presented in the XIV Italian Meeting of Game Theory and Applications (July 11-14, 2001)
Matsuhisa, T.: Communication leading to a Nash equilibrium without acyclic condition (S4-knowledge case). In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J.J. (eds.) ICCS 2004. LNCS, vol. 3039, pp. 884–891. Springer, Heidelberg (2004)
Matsuhisa, T.: Bayesian communication under rough sets information. In: Butz, C.J., et al. (eds.) IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology. WI-ITA 2006 Workshop Proceedings, pp. 378–381. IEEE Computer Society, Los Alamitos (2006)
Matsuhisa, T., Strokan, P.: Bayesian belief communication leading to a Nash equilibrium in belief. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 299–306. Springer, Heidelberg (2005)
Monderer, D., Samet, D.: Approximating common knowledge with common beliefs. Games and Economic Behaviors 1, 170–190 (1989)
Nash, J.F.: Equilibrium points in n-person games. In: Proceedings of the National Academy of Sciences of the United States of America, vol. 36, pp. 48–49 (1950)
Parikh, R., Krasucki, P.: Communication, consensus, and knowledge. Journal of Economic Theory 52, 178–189 (1990)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Matsuhisa, T. (2007). Communication Leading to Nash Equilibrium Through Robust Messages – S5-Knowledge Model Case –. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-73556-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73555-7
Online ISBN: 978-3-540-73556-4
eBook Packages: Computer ScienceComputer Science (R0)