Abstract
We suggest two new notions of game equilibrium for arbitrary conflict problems (antagonistic, noncooperative, cooperative, static, and dynamic ones), which permit one to find a unique strongest equilibrium in some cases in which it is impossible to find such a solution with the use of all earlier known notions of equilibrium.
Similar content being viewed by others
References
Smol’yakov, E.R., Strong Equilibrium for Conflict Problems, Differ. Uravn., 2008, vol. 44, no. 11, pp. 1566–1575.
Smol’yakov, E.R., Teoriya konfliktnykh ravnovesii (Theory of Conflict Equilibria), Moscow: Editorial URSS, 2005.
Nash, J., Non-Cooperative Games, Ann. of Math., 1951, vol. 54, no. 2, pp. 286–295.
Vorob’ev, N.N., Osnovy teorii igr. Beskoalitsionnye igry (Principles of Game Theory: Noncooperative Games), Moscow: Nauka, 1984.
Vaisbord, E.M. and Zhukovskii, V.I., Vvedenie v differentsial’nye igry neskol’kikh lits i ikh prilozheniya (Introduction to Differential n-Person Games and Their Applications), Moscow: Sovet. Radio, 1980.
Smol’yakov, E.R., Concepts of Cooperative Conflict Equilibria, Differ. Uravn., 2006, vol. 42, no. 11, pp. 1539–1548.
Smol’yakov, E.R., An Expanded Base System of Conflict Equilibria, Dokl. Akad. Nauk, 2006, vol. 409, no. 2, pp. 163–166.
Smol’yakov, E.R., Strengthened Equilibria for Conflict Problems, Dokl. Akad. Nauk, 2007, vol. 415, no. 3, pp. 318–321.
Smol’yakov, E.R., Auxiliary Strong Equilibria for Dynamic Conflict Problems, Differ. Uravn., 2007, vol. 43, no. 11, pp. 1497–1506.
Smol’yakov, E.R., Unique Fair Division in Static and Dynamic Cooperative Games, Differ. Uravn., 2007, vol. 43, no. 12, pp. 1637–1648.
Varga, J., Optimal Control for Differential and Functional Equations, John Wiley, 1969. Translated under the title Optimal’noe upravlenie differentsial’nymi i funktsional’nymi uravneniyami, Moscow: Nauka, 1977.
Author information
Authors and Affiliations
Additional information
Original Russian Text © E.R. Smol’yakov, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 5, pp. 752–760.
Rights and permissions
About this article
Cite this article
Smol’yakov, E.R. Complicated equilibria for game problems. Diff Equat 45, 768–777 (2009). https://doi.org/10.1134/S0012266109050164
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266109050164