Abstract
A number of solution concepts of normal-form games have been proposed in the literature on subspaces of action profiles that have Nash type stability. While the literature mainly focuses on the minimal of such stable subspaces, this paper argues that non-minimal stable subspaces represent well the multi-agent situations to which neither Nash equilibrium nor rationalizability may be applied with satisfaction. As a theoretical support, the authors prove the optimal substructure of stable subspaces regarding the restriction of a game. It is further argued that the optimal substructure characterizes hierarchical diversity of coordination and interim phases in learning.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Kalai and D. Samet, Persistent equilibria in strategic games, International Journal of Game Theory, 1984, 13(3): 129–144.
K. Basu and J. W. Weibull, Strategy subsets closed under rational behavior, Economic Letters, 1991, 36(2): 141–146.
M. Voorneveld, Preparation, Games and Economic Behavior, 2004, 48(2): 403–414.
A. Rubinstein and A. Wolinsky, Rationalizable conjectural equilibrium: Between nash and rationalizability, Games and Economic Behavior, 1994, 6(2): 299–311.
D. Bernheim, Rationalizable strategic behavior, Econometrica, 1984, 52(4): 1007–1028.
D. Pearce, Rationalizable strategic behavior and the problem of perfection, Econometrica, 1984, 52(4): 1029–1050.
M. Gilli, On non-nash equilibria, Games and Economic Behavior, 1999, 27(2): 184–203.
D. Fudenberg and D. K. Levine, Limit games and limit equilibria, Journal of Economic Theory, 1986, 38(2): 261–279.
T. Schelling, The Strategy of Conflict, Harvard University Press, Cambridge, 1960.
M. Aoki, Toward a Comparative Institutional Analysis, MIT Press, Cambridge, 2001.
A. Rubinstein, Economics of Language, Cambridge University Press, Cambridge, 2000.
K. Binmore and L. Samuelson, The evolution of focal points, Games and Economic Behavior, 2006, 55(1): 21–42.
R. J. Aumann and A. Brandenburger, Epistemic conditions for Nash equilibrium, Econometrica, 1995, 63(5): 1161–1180.
S. Chatterji and S. Ghosal, Local coordination and market equilibria, Journal of Economic Theory, 2004, 114(2): 255–279.
C. Harsanyi John and R. Selten, A General Theory of Equilibrium Selection, MIT Press, Cambridge, 1988.
E. Kalai and E. Lehrer, Rational learning leads to Nash equilibrium, Econometrica, 1993, 61(5): 1019–1045.
D. Fudenberg and D. K. Levine, The Theory of Learning in Games, MIT Press, Cambridge, 1998.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kobayashi, N., Kijima, K. Optimal substructure of set-valued solutions of normal-form games and coordination. J Syst Sci Complex 22, 63–76 (2009). https://doi.org/10.1007/s11424-009-9147-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-009-9147-9