B. B. Akhmetov, V. A. Lakhno, V. P. Malyukov


Actuality. There is considered the actual problem of an optimal decision making on financing of information and cyber security
means in the conditions of active counteraction to the side of the attackers of information and communication systems of the logistics
and situational transport center. The aim of the work is to develop a model for the decisions support system of the financing process of the information and cyber security means of the logistics and situational transport center in conditions of active counteraction to the attacking party, which differs from existing approaches by solving a bilinear differential quality game with several terminal surfaces.
Method. Solving a bilinear differential quality game, that allows to reflect adequately the essence of the problem, there was used
a discrete approximation method. The method allowed not only to find a solution of the bilinear differential quality game with
dependent motions, but also became an effective at the software implementation of the decisions support system in the field of
financing information and cyber security means for information and communication systems of the protected logistics-situational
transport center.
Results. The developed model allows to obtain optimal financing strategies by the cyber security means protection side for
information and communication logistics and situational transport centers at any ratio of parameters describing the financing process,
no matter how financially the party tries to attack the security perimeters.
Conclusions. In this article there was firstly considered the model within the framework of the bilinear differential quality game
scheme for the decisions support system of the process of cyber security means financing for information and communication
systems of protected logistics and situational transport centers. For such differential games there were previously developed no
effective solution methods. In the proposed solution there were firstly used the differential equations that define the interaction
dynamics, describe the dependent motions by means of bilinear functions.


cyber security; differential game; optimal strategies; hacking and protection; decision support system.


Manshaei M. H., Zhu Q., Alpcan T. et al. Game theory meets network security and privacy, ACM Computing Surveys, 2013, Vol. 45, No. 3, pp. 1–39. DOI: 10.1145/2480741.2480742

Grossklags J., Christin N., Chuang J. Secure or insure?: a gametheoretic analysis of information security games,17th

international conference on World Wide Web, Beijing, China,

– 25 April 2008 : proceedings.New York, ACM, 2008. pp.

–218. DOI:10.1145/1367497.1367526

Cavusoglu H., MishraB., Raghunathan S. A model for

evaluating IT security investments, Communications of the

ACM, 2004, Vol. 47, No. 7, pp. 87–92.

FielderA., PanaousisE., Malacaria P. et al.Decision support

approaches for cyber security investment,Decision Support

Systems, 2016, Vol. 86, pp. 13–23. DOI:


Meland P. H., Tondel I. A., Solhaug B. Mitigating risk with

cyberinsurance, IEEE Security & Privacy, 2015, No. 13(6), pp.

–43. DOI: 10.1109/MSP.2015.137

Malyukov V.P. A differential game of quality for two groups of objects, Journal of Applied Mathematics and Mechanics, 1991, Vol. 55, No.5, pp. 596–606.7. Lavrent'ev A.V., Zjazin V. P. O primenenii metodov teorii igr

dlja reshenija zadach komp'juternoj bezopasnosti, Bezopasnost' informacionnyh tehnologij, 2013, No. 3, pp. 19–24.

Bykov A. Ju., Altuhov N. O., Sosenko A. S. Zadacha vybora

sredstv zashhity informacii v avtomatizirovannyh sistemah na

osnove modeli antagonisticheskoj igry, Inzhenernyj vestnik,

, No. 4 , pp. 525–542.

Basalova G. V., Sychugov A. A. Primenenie metodov teorii igr dlja optimizacii vybora sredstv zashhity informacii, Izvestija

Tul'skogo gosudarstvennogo universiteta, Tehnicheskie nauki,

, No. 11(1), pp. 122–128.

FielderA., PanaousisE., MalacariaP. etal. Game theory meets information security management, IFIP International

Information Security Conference, Marrakech, Morroco, 2–4

June 2014 : proceedings, Berlin, Springer, 2014, pp.15–29.


Zarkumova R. N. Primenenie metodov teorii igr pri vybore

sredstva jeffektivnoj zashhity, Sbornik nauchnyh trudov

Novosibirskogo gosudarstvennogo tehnicheskogo universiteta,

, No. 4, pp. 41–46.

Gao X., ZhongW., MeiS. A game-theoretic analysis of

information sharing and security investment for complementary firms, Journal of the Operational Research Society, 2014, Vol. 65, No. 11, pp. 1682–1691. DOI:10.1057/jors.2013.13

Lahno V.A. Model' intellektual'noj sistemy upravlenija

gorodskimi avtobusnymi perevozkami, Radio Electronics,

Computer Science, Control, 2016, No. 2, pp. 119–127. DOI:


Malyukov V.P. Discrete-approximation method for solving a bilinear differential game, Cybernetics and Systems Analysis,

,Vol. 29, No. 6, pp. 879 – 888.

Lakhno V., Malyukov V., Gerasymchuk N. et al. Development of the decision making support system to control a procedure of financial investment, Eastern-European Journal of Enterprise Technologies, 2017, Vol. 6, No. 3, pp. 24–41. DOI:10.15587/1729-4061.2017.119259

Lakhno V. A. Development of a support system for managing the cyber security, Radio Electronics, Computer Science, Control, 2017, No. 2, pp. 109–116. DOI: 10.15588/1607-3274-2017-2-12

Smeraldi F., Malacaria P. How to spend it: optimal investment for cyber security, 1st International Workshop on Agents and CyberSecurity, Paris, France, 06–08 May 2014 : proceedings, New York, ACM, 2014, pp. 8. DOI: 10.1145/2602945.2602952

Tosh D. K., Molloy M., Sengupta S. et al.Cyber-investment and cyber-information exchange decision modeling, High

Performance Computing and Communications IEEE 7th

International Symposium on Cyberspace Safety and Security

(CSS), New York, 24–26 August 2015 : proceedings, New

York, IEEE, 2015, pp. 1219–1224. DOI: 10.1109/HPCC-CSSICESS. 2015.264

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