Abstract
The author proposes new concepts of equilibria. Though they have a complex description, they are very useful to find the unique solution in game problems (static and dynamic), including the cases where some known equilibria, important for finding the solution, are empty.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Isaacs, Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, Dover Books on Mathematics, Dover Publ. (1999).
J. C. C. McKinsey, Introduction to the Theory of Games (Dover Books on Mathematics), Dover Publ. (2003).
J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton Univ. Press (1944).
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russian], Nauka, Moscow (1974).
A. B. Kurzhanskii, Control and Observation under Uncertainty [in Russian], Nauka, Moscow (1977).
N. N. Petrov, Game Theory [in Russian], Udmurtskii Univ., Izhevsk (1977).
E. M. Vaisbord and V. I. Zhukovskii, An Introduction into Multiperson Differential Games and their Application [in Russian], Sov. Radio, Moscow (1980).
N. N. Vorob’ev, Fundamentals of Game Theory. Coalition-Free Games [in Russian], Nauka, Moscow (1984).
L. A. Petrosyan and T. I. Kuz’mina, Coalition-Free Differential Games [in Russian], Irkutsk. Gos. Univ., Irkutsk (1989).
A. A. Chikrii, Conflict-Controlled Processes [in Russian], Naukova Dumka, Kyiv (1992).
E. R. Smol’yakov, Control of Conflicts with Side Interests of the Players [in Russian], LAP LAMBERT Acad. Publ., Saarbrucken (2013).
E. R. Smol’yakov, Theory of Antagonisms and Differential Games [in Russian], Editorial URSS, Moscow (2000).
E. R. Smol’yakov, Theory of Conflict Equilibria [in Russian], Editorial URSS, Moscow (2005).
E. R. Smol’yakov, Methods to Solve Conflict Problems [in Russian], MGU, Moscow (2010).
E. R. Smol’yakov, Generalized Optimal Control and Dynamic Conflict Problems [in Russian], MGU, Moscow (2010).
E. R. Smol’yakov, Equilibrium Models in Case of Mismatched Interests of Players [in Russian], Nauka, Moscow (1986).
V. V. Podinovskii and V. D. Nogin, Pareto-Optimal Solutions of Multicriteria Problems [in Russian], Nauka, Moscow (1982).
E. R. Smol’yakov, “Weakened concepts of equilibrium and optimality in conflict problems,” Differ. Uravn., 49, No. 3, 373–379 (2013).
J. Warga, Optimal Control of Differential and Functional Equations, Academic Press (1972).
Author information
Authors and Affiliations
Corresponding author
Additional information
*The study was supported by the Program of Basic Research ONIT RAN and Russian Foundation for Basic Research No. 15–01–08838–a.
Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2015, pp. 107–118.
Rights and permissions
About this article
Cite this article
Smol’yakov, E.R. Combined Equilibria for Conflict Problems* . Cybern Syst Anal 51, 929–938 (2015). https://doi.org/10.1007/s10559-015-9785-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-015-9785-y