Mean-Field-Game Model for Botnet Defense in Cyber-Security

Applied Mathematics and Optimization

Volumn 74, Issue 3, 2016, Pages 669-692

  Kolokoltsov, V N ^a,b   Bensoussan, A ^c,d,e  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b INSTITUTE OF INFORMATICS PROBLEMS   (Russian Federation)

^c UNIVERSITY OF TEXAS AT DALLAS   (United States)

^d HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^e Ajou University   (South Korea)

Author keywords

Botnet defence; Mean field game; Phase transitions; Stable equilibrium

Indexed keywords

COMPUTER GAMES; DECISION MAKING; PERSONAL COMPUTING; PHASE TRANSITIONS; RANDOM PROCESSES; STOCHASTIC SYSTEMS;

BOTNET DEFENCE; DECISION MAKING PROCESS; DEFENCE SYSTEMS; INFECTION RATES; INTERACTING AGENTS; MEAN FIELD GAMES; STABLE EQUILIBRIUM; STOCHASTIC GAME;

MALWARE;

EID: 84994460480     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-016-9389-6     Document Type: Article

References (27)

1. Bardi, M., Caines, P., Dolcetta, I.C.: Preface: DGAA special issue on mean field games. Dyn. Games Appl. 3(4), 443–445 (2013)
2. Basna, R., Hilbert, A., Kolokoltsov, V.: An epsilon-Nash equilibrium for non-linear Markov games of mean-field-type on finite spaces. Commun. Stoch. Anal. 8(4), 449–468 (2014)
3. Bauso, D., Tembine, H., Basar, T.: Robust mean-field games. Dyn. Games Appl. 6, (2015). doi:10.1007/s13235-015-0160-4
4. Bensoussan, A., Frehse, J., Yam, P.: Mean Field Games and Mean Field Type Control Theory. Springer, New York (2013)
5. Bensoussan, A., Hoe, S., Kantarcioglu, M.: A game-theoretical approach for finding optimal strategies in a botnet defense model. In: Alpcan T., Buttyan, L., Baras, J. (eds.)Proceeding of the Decision and Game Theory for Security First International Conference, GameSec: Berlin, Germany, November 22–23, 2010, vol. 6442, pp. 135–148 (2010)
6. Caines, P. E.: Mean Field Games, Encyclopedia of Systems and Control. In: Samad, T., Ballieul, J. (eds.) Springer Reference 364780. Springer, London (2014). doi: 10.1007/978-1-4471-5102-930-1
7. Cardaliaguet, P., Lasry, J.-M., Lions, P.-L., Porretta, A.: Long time average of mean field games with a nonlocal coupling. SIAM J. Control Optim. 51(5), 3558–3591 (2013)
8. Carmona, R., Lacker, D.: A probabilistic weak formulation of mean field games and applications. Ann. Appl. Probab. 25(3), 1189–1231 (2015)
9. Carmona, R., Delarue, F.: Probabilistic analysis of mean-field games. SIAM J. Control Optim. 514, 2705–2734 (2013)
10. Doncel, J., Gast, N., Gaujal, B.: Mean-Field Games with Explicit Interactions. Preprint. https://hal.inria.fr/hal-01277098/file/main
11. Gomes, D.A., Mohr, J., Souza, R.R.: Discrete time, finite state space mean feld games. J. Math. Pures Appl. 93(3), 308–328 (2010)
12. Gomes, D.A., Mohr, J., Souza, R.R.: Continuous time finite state space mean feld games. Appl. Math. Optim. 68(1), 99–143 (2013)
13. Gomes, D.A., Saude, J.: Mean field games models - a brief survey. Dyn. Games Appl. 4(2), 110–154 (2014)
14. Guéant, O., Lasry, J.-M., Lions, P.-L.: Mean Field Games and Applications. Paris-Princeton Lectures on Mathematical Finance 2010. Lecture Notes in Mathematics, pp. 205–266. Springer, Berlin (2003)
15. Huang, M., Malhamé, R., Caines, P.: Large population stochastic dynamic games: closed-loop Mckean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6, 221–252 (2006)
16. Huang, M., Caines, P., Malhamé, R.: Large-population cost-coupled LQG Problems with nonuniform agents: individual-mass behavior and decentralized ϵ -Nash equilibria. IEEE Trans. Automat. Control 52(9), 1560–1571 (2007)
17. Kolokoltsov, V.N.: Nonlinear Markov processes and kinetic equations. Cambridge Tracks in Mathematics 182, Cambridge University. Press, 2010. See the review of Prof. D. Applebaum in. Bulletin of the London Mathematical Society vol. 43(6), pp. 1245–1247 (2011)
18. Kolokoltsov, V. N.: Nonlinear Markov games on a finite state space (mean-field and binary interactions). Int. J. Stat. Probab. 1:1 (2012), 77-91. http://www.ccsenet.org/journal/index.php/ijsp/article/view/16682
19. Kolokoltsov, V. N.: The evolutionary game of pressure (or interference), resistance and collaboration (2014). arxiv:1412.1269 (to appear in Mathematics of Operatoion Research (MOR))
20. Kolokoltsov, V. N., Malafeyev, O. A.: Mean field game model of corruption. Dyn. Games Appl. (2015). doi: 10.1007/s13235-015-0175-x (published with Open Access)
21. Kolokoltsov, V. N., Malafeyev, O. A.: Corruption and botnet defense: a mean field game approach arXiv:1607.07350
22. Kolokoltsov, V., Troeva, M., Yang, W.: On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players. Dyn. Games Appl. 4(2), 208–230 (2014)
23. Lasry, J.-M., Lions, P.-L.: Jeux à champ moyen. I. Le cas stationnaire (French). C.R. Math. Acad. Sci. Paris 343(9), 619–625 (2006)
24. Li, Z., Liao, Q., Striegel, A.: Botnet Economics: Uncertainty Matters. http://weis2008.econinfosec.org/papers/Liao
25. Liu, J., Tang, Y., Yang, Z. R.: The spread of disease with birth and death on networks. J. Stat. Mech. (2004). arXiv:q-bio/0402042v3
26. Lye, K.-W., Wing, J.M.: Game strategies in network security. Int. J. Inf. Secur. 4, 71–86 (2005)
27. Tembine, H., Zhu, Q., Basar, T.: Risk-sensitive mean-field games. IEEE Trans. Automat. Control 59(4), 835–850 (2014)