Abstract
The interaction of many participants dividing among themselves a resource located on a certain set is investigated. For the problem stated, the Mash equilibrium does not exist in most of the cases, but at the same time there is an intuitively perceived stable rational behavior of participants, which relies on the reflexive accounting of mutual threats. For the description of such a behavior, the definition is set up of an equilibrium in safe strategies (ESS’s), which coincides with the strict Nash equilibrium where it is available and exists for those situations in the stated problem where it is unavailable. Using the introduced definition, the initial problem is examined. The introduced equilibrium is also illustrated by examples of bimatrix games, a competitive system of stimulation, and a game in which the ESS’s does not exist.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Aleskerov, F.T. and Orteshuk, P., Vybory. Golosovanie. Partii (Elections, Voting, Parties), Moscow: Akademiya, 1995.
Downs, A., An Economic Theory of Democracy, New York: Harper and Row, 1957.
Mas-Collel, A., Whinston, M.D., and Green, G.R., Microeconomic Theory, New York: Oxford Univ. Press, 1995.
Brams, S.J. and Taylor, A.D., Win-Win Solution Guaranteeing Fair Shares to Everybody, NewYork: W.W. Norton and Co., 1999.
Sandak, N.N., Competitive Systems, in Aktivnye sistemy, no. 2 “Problemy i metody upravleniya v aktivnykh sistemakh” (Active Systems. Collection of Articles no. 2 “Problems and Methods of Control in Active Systems,”) Moscow: Inst. Probl. Upravlen., 1974, pp. 86–98.
Smol’yakov, E.R., An Extended Basic System of Equilibria and the Technique of a Solution of Noncooperative Games, Avtom. Telemekh., 2001, no. 11, pp. 145–153.
Novikov, D.A. and Chkhartishvili, A.G., Refleksivnye igry, Seria “Upravlenie organizatsionnymi sistemami” (Reflexive Games. Series “Control of Organizational Systems”), Moscow: SINTEG, 2003.
Novikov, D.A. and Tsvetkov, A.V., Mekhanizmy stimulirovaniya v mnogoelementnykh organizatsionnykh sistemakh (Stimulation Mechanisms in Multicomponent Organizational Systems), Moscow: Apostrof, 2000.
Vasil’ev, D.K., Zalozhnev, A.Yu., Novikov, D.A., and Tsvetkov, A.V., Tipovye resheniya v upravlenii proektami (Typical Solutions in Control of Projects), Moscow: Inst. Probl. Upravlen., 2003.
Tsyganov, V.V., Adaptivnye mekhanizmy v otraslevom upravlenii (Adaptive Mechanisms in Branch Control), Moscow: Nauka, 1991.
Smol’yakov, E.R., Heuristic Procedures of Search for Equilibria in Noncooperative and Two-Person Zero-Sum Games, Avtom. Telemekh., 1996, no. 3, pp. 18–28.
Author information
Authors and Affiliations
Additional information
Translated from Avtomatika i Telemekhanika, No. 3, 2005, pp. 139–153.
Original Russian Text Copyright © 2005 by Iskakov.
This paper was recommended for publication by D.A. Novikov, a member of the Editorial Board
Rights and permissions
About this article
Cite this article
Iskakov, M.B. Equilibrium in safe strategies. Autom Remote Control 66, 465–478 (2005). https://doi.org/10.1007/s10513-005-0076-3
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10513-005-0076-3