Abstract
A new optimality principle is proposed that generalizes the Stackelberg equilibrium principle. Its connection with the classical definition is investigated. The technique of working with the new definition is discussed. As an example, solutions are found in two hierarchical games with feedback.
Similar content being viewed by others
REFERENCES
Burkov, V.N. and Enaleev, A.K., Optimality of the fair play principle. Necessary and sufficient conditions for information reliability in active systems, Autom. Remote Control, 1985, vol. 46, no. 3 part 1, pp. 341–348.
Vasin, A.A. and Morozov, V.V., Vvedenie v teoriyu igr s prilozheniyami k ekonomike (Introduction to Game Theory with Applications to Economics), Moscow: MAKS-Press, 2003.
Vatel’, I.A. and Ereshko, F.I., Matematika konflikta i sotrudnichestva (The Mathematics of Conflict and Cooperation), Moscow: Znanie, 1973.
Germeier, Yu.B., On games of two persons with a fixed sequence of moves, Dokl. Akad. Nauk SSSR, 1971, vol. 198, no. 5, pp. 1001–1004.
Germeier, Yu.B., Vvedenie v teoriyu issledovaniya operatsii (Introduction to Operations Research Theory), Moscow: Nauka, 1971.
Germeier, Yu.B., Nonantagonistic Games, Dordrecht: D. Reidel, 1986.
Gorelik, V.A. and Kononenko, A.F., Teoretiko-igrovye modeli prinyatiya reshenii v ekologo-ekonomicheskikh sistemakh (Game-Theoretic Decision-Making Models in Ecological-Economic Systems), Moscow: Radio Svyaz’, 1982.
Gorelov, M.A., Maximal guaranteed result for limited volume of transmitted information, Autom. Remote Control, 2011, vol. 72, no. 3, pp. 580–599.
Gorelov, M.A., Maximal guaranteed result in hierarchical games, Upr. Bol’shimi Sist., 2017, no. 67, pp. 4–31.
Kononenko, A.F., The role of information on the opponent’s target function in a two-person game with a fixed sequence of moves, USSR Comput. Math. Math. Phys., 1973, vol. 13, no. 2, pp. 49–56.
Kukushkin, N.S. and Morozov, V.V., Teoriya neantagonisticheskikh igr (Theory of Nonzero-Sum Games), Moscow: Izd. Mosk. Gos. Univ., 1984.
Moulin, H., Théorie des jeux pour l’économie et la politique, Paris: Hermann, 1981. Translated under the title: Teoriya igr s primerami iz matematicheskoi ekonomiki, Moscow: Mir, 1985.
Zermelo, E., Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proc. Fifth Congress Math. (Cambridge, 1912), Cambridge: Cambridge Univ. Press, 1913, pp. 501–504.
Burkov, V.N. and Lerner, A.Ya., Fairplay in control of active systems, in Differential Games and Related Topics, Amsterdam–London: North-Holland, 1971, pp. 164–168.
De Méziriac, B., Problèmes plaisants et délectables, qui se sont par les nombres, Lion, 1612.
Simaan, M. and Cruz, J.B., On the Stackelberg strategy in nonzero-sum games, J. Optim. Theory Appl., 1973, vol. 11, no. 5, pp. 533–555.
Von Stackelberg, H., Market Structure and Equilibrium, 1st Ed. Translation into English, Berlin–Heidelberg: Springer-Verlag, 2011.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by V. Potapchouck
Rights and permissions
About this article
Cite this article
Gorelov, M.A. Hierarchical Games with Feedback under the Assumption of Benevolence of the Lower-Level Player. Autom Remote Control 83, 437–452 (2022). https://doi.org/10.1134/S0005117922030110
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117922030110