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JOURNALS // Computer Research and Modeling

Computer Research and Modeling, 2020, Volume 12, Issue 3, Pages 653–667 (Mi crm808)

Numerical method for finding Nash and Shtakelberg equilibria in river water quality control models
M. A. Reshitko, G. A. Ougolnitsky, A. B. Usov

References

1. Byudzhetnyi kodeks Rossiiskoi Federatsii, http://pravo.gov.ru/proxy/ips/?docbody=&nd=102054721 (in Russian) (accessed: 16.01.2020)
2. V. Burkov, V. Opoitsev, “Metagamery approach to the management of hierarchical systems”, Automation and Remote Control, 1974, no. 1, 103–114 (in Russian)  mathnet  mathscinet  zmath
3. Yu. Germeier, I. Vatel, “Games with a hierarchical vector of interests”, Izvestiya AN SSSR. Tekhnicheskaya kibernetika, 1974, no. 3, 54–69 (in Russian)  mathscinet  mathscinet  zmath
4. V. Gorelik, M. Gorelov, A. Kononenko, Analysis of conflict situations in control systems, Moscow, 1991 (in Russian)  mathscinet
5. M. A. Gorelov, A. F. Kononenko, “Dynamic models of conflicts. III. Hierarchical games”, Automation and Remote Control, 2014, no. 76, 264–277  mathnet  mathscinet  zmath  elib
6. V. Kogai, S. Fadeev, “Application of continuation in a parameter based on the multiple shooting method for the numerical study of nonlinear boundary value problems”, Sibirskii zhurnal industrial’noi matematiki, 4:1 (7) (2001), 83–101 (in Russian)  mathnet  mathscinet
7. V. Malkin, “Solution of a twopoint boundary value problem by a non-gradient random search method”, Sistemnyi analiz i prikladnaya informatika, 2001, no. 1, 20–34 (in Russian)
8. Postanovlenie Pravitel’stva RF ot 03.03.2017 No. 255 (red. ot 27.12.2019) “Ob ischislenii i vzimanii platy za negativnoe vozdeistvie na okruzhayushchuyu sredu”, http://www.consultant.ru/document/cons_doc_LAW_213744/aed3a10937b9f8c79b9b9b5bdc08a8a31296c43d (in Russian) (accessed: 16.01.2020)
9. Postanovlenie Pravitel’stva RF ot 13.09.2016 “O stavkakh platy za negativnoe vozdeistvie na okruzhayushchuyu sredu i dopolnitel’nykh koeffitsientakh”, http://pravo.gov.ru/proxy/ips/?docbody=&nd=102409476 (in Russian) (accessed: 16.01.2020)
10. G. Ugolnitskii, Management of sustainable development of active systems, Izdatel’stvo Yuzhnogo federal’nogo universiteta, Rostov-na-Donu, 2016, 940 pp. (in Russian)  mathscinet
11. G. A. Ugol’nitskii, A. B. Usov, “Equilibria in models of hierarchically organized dynamic systems with regard to sustainable development conditions”, Automation and Remote Control, 6:75 (2014), 1055–1068  mathnet  mathscinet  zmath  elib
12. G. Ugolnitskii, A. Usov, “Dynamic hierarchical two-person games in software strategies and their applications”, Matematicheskaya teoriya igr i ee prilozheniya, 5:2 (2013), 82–104 (in Russian)  mathnet  mathscinet  zmath
13. G. A. Ugol’nitskii, A. B. Usov, “Solution algorithms for differential models of hierarchical control systems”, Automation and Remote Control, 77:5 (2016), 872–880  mathnet  crossref  mathscinet  elib  scopus
14. S. Fadeev, “The program for the numerical solution of nonlinear boundary value problems for systems of ordinary differential equations with a parameter”, Vychislitel’nye metody lineinoi algebry, 1990, 104–200, Nauka, Sibirskoe otdelenie, Novosibirsk (in Russian)  mathscinet
15. Federal’nyi zakon ot 10.01.2002 No. 7-FZ (red. ot 27.12.2019) «Ob okhrane okruzhayushchei sredy». Stat’ya 16, http://www.consultant.ru/document/cons_doc_LAW_34823/4d2f994d3199b20f35934603e85132412705d121/ (in Russian) (accessed: 16.01.2020)
16. T. Basar, G. J. Olsder, Dynamic Noncooperative Game Theory, Philadelphia, SIAM, 1999  mathscinet  zmath
17. E. Dockner, S. Jorgensen, N. V. Long, G. Sorger, Differential Games in Economics and Management Science, Cambridge University Press, 2000  mathscinet  zmath
18. R. Helmer, I. Hespanhol, Water Pollution Control. A Guide to the Use of Water Quality Management Principles, St. Edmundsbury Press, 1997
19. H. B. Keller, Numerical methods for two-point boundary-value problems, Courier Dover Publications, 2018  mathscinet
20. A. V. Rao, “A Survey of Numerical Methods for Optimal Control”, Advances in the Astronautical Sciences, 135 (2009), 497–528
21. G. Ugolnitskii, A. Usov, “Computer Simulations as a Solution Method for Differential Games”, Computer Simulations: Advances in Research and Applications, eds. M. D. Pfeffer and E. Bachmaier, Nova Science Publishers, NY, 2018, 63–106


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