Logic in the study of hierarchical games under uncertainty
Tóm tắt
We study a hierarchical game of two players with an uncertain factor. We consider the case of interval uncertainty. Under the assumption that the set of uncertain factors is finite, we compute the maximal guaranteed result of the top level player. Under standard topological assumptions we find a lower bound for this result.
Tài liệu tham khảo
Germeier, Yu.B. and Moiseev, N.N., On Some Problems of the Theory of Hierarchical Systems, in Problemy prikladnoi matematiki i mekhaniki (Problems of Applied Mathematics and Mechanics), Moscow: Nauka, 1971, pp. 30–43.
Gorelik, V.A., Gorelov, M.A., and Kononenko, A.F., Analiz konfliktnykh situatsii v sistemakh upravleniya (Analysis of Confict Situations in Control Systems), Moscow: Radio i Svyaz’, 1991.
Kononenko, A.F., Khalezov, A.D., and Chumakov, V.V., Prinyatie reshenii v usloviyakh neopredelennosti (Decision Making under Uncertainty), Moscow: Vychisl. Tsentr Akad. Nauk SSSR, 1991.
Gorelov, M.A., Hierarchical Games with Uncertain Factors, Upravlen. Bol’shimi Sist., 2016, no. 59, pp. 6–22.
Germeier, Yu.B., Vvedenie v teoriyu issledovaniya operatsii (Introduction to Operations Research Theory), Moscow: Nauka, 1971.
Burkov, V.N., Osnovy teorii aktivnykh sistem (Fundamentals of the Theory of Active Systems), Moscow: Nauka, 1977.
Burkov, V.N. and Novikov, D.A., Teoriya aktivnykh sistem: sostoyanie i perspektivy (Theory of Active Systems: State of the Art and Future Directions), Moscow: Sinteg, 1999.
Novikov, D.A., Teoriya upravleniya organizatsionnymi sistemami (Control Theory for Organizational Systems), Moscow: MPSI, 2005.
Bolton, P. and Dewatripont, M., Contract Theory, Cambridge: MIT Press, 2004.
Laffont, J.-J. and Martimort, D., The Theory of Incentives: The Principal-Agent Model, Cambridge: MIT Press, 2002.
Gorelov, M.A., Maximal Guaranteed Result for Limited Volume of Transmitted Information, Autom. Remote Control, 2011, vol. 72, no. 3, pp. 580–599.
Vereshchagin, N.K. and Shen’, A., Yazyki i ischisleniya (Languages and Calculi), Moscow: MTsNMO, 2012.
Bremzen, A.S. and Guriev, S.M., Konspekty lektsii po teorii kontraktov (Lecture Notes on Contract Theory), Moscow: Rossiiskaya Ekonomicheskaya Shkola, 2005.
Gorelov, M.A., Institutional Control Model, Upravlen. Bol’shimi Sist., 2011, no. 35, pp. 68–93.
Enaleev, A.K., Optimal Consistent Mechanisms in Active Systems and Problem of Contract Theory, Upravlen. Bol’shimi Sist., 2014, no. 49, pp. 167–182.
Gorelov, M.A., Hierarchical Games with Random Factors, Upravlen. Bol’shimi Sist., 2016, no. 63, pp. 87–105.