Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/mean-field-game-model-for-botnet-defense-in-cyber-security-dpOqIK6BQt
References (33)
-
M. Bardi, P. Caines, I. Dolcetta (2013)
Preface: DGAA 2nd Special Issue on Mean Field GamesDynamic Games and Applications, 4
-
P. Cardaliaguet, J. Lasry, P. Lions, A. Porretta (2013)
Long Time Average of Mean Field Games with a Nonlocal CouplingSIAM J. Control. Optim., 51
-
P. Caines, Minyi Huang, R. Malhamé (2006)
Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principleCommun. Inf. Syst., 6
-
Z. Li, Qi Liao, A. Striegel (2008)
Botnet Economics: Uncertainty Matters -
A. Bensoussan, J. Frehse, Phillip Yam (2013)
Mean Field Games and Mean Field Type Control Theory -
Kong-wei Lye, Jeannette Wing (2005)
Game strategies in network securityInternational Journal of Information Security, 4
-
DA Gomes, J Mohr, RR Souza (2013)
Continuous time finite state space mean feld gamesAppl. Math. Optim., 68
-
V. Kolokoltsov, O. Malafeyev (2015)
Mean-Field-Game Model of CorruptionDynamic Games and Applications, 7
-
J. Liu, E. al. (2004)
The spread of disease with birth and death on networksJournal of Statistical Mechanics: Theory and Experiment, 2004
-
J. Lasry, P. Lions (2006)
Jeux à champ moyen. I – Le cas stationnaireComptes Rendus Mathematique, 343
-
H. Tembine, Quanyan Zhu, T. Başar (2012)
Risk-Sensitive Mean-Field GamesIEEE Transactions on Automatic Control, 59
-
(2010)
Lasry and P-L -
A. Bensoussan, Murat Kantarcioglu, S. Hoe (2010)
A Game-Theoretical Approach for Finding Optimal Strategies in a Botnet Defense Model -
O Guéant, J-M Lasry, P-L Lions (2003)
Mean Field Games and Applications. Paris-Princeton Lectures on Mathematical Finance 2010 -
M Huang, P Caines, R Malhamé (2007)
Large-population cost-coupled LQG Problems with nonuniform agents: individual-mass behavior and decentralized $$\epsilon $$ ϵ -Nash equilibriaIEEE Trans. Automat. Control, 52
-
V. Kolokoltsov (2014)
The Evolutionary Game of Pressure (or Interference), Resistance and CollaborationMath. Oper. Res., 42
-
R. Carmona, F. Delarue (2012)
Probabilistic Analysis of Mean-Field GamesSIAM J. Control. Optim., 51
-
R. Carmona, D. Lacker (2013)
A probabilistic weak formulation of mean field games and applicationsAnnals of Applied Probability, 25
-
D. Gomes, J. Mohr, Rafael Souza (2012)
Continuous Time Finite State Mean Field GamesApplied Mathematics & Optimization, 68
-
J-M Lasry, P-L Lions (2006)
Jeux à champ moyen. I. Le cas stationnaire (French)C.R. Math. Acad. Sci. Paris, 343
-
D. Applebaum (2011)
Nonlinear Markov processes and kinetic equations (Cambridge Tracts in Mathematics 182)Bulletin of The London Mathematical Society, 43
-
W. Zhang (2017)
In discrete Time -
V. Kolokoltsov (2010)
Nonlinear Markov Processes and Kinetic Equations -
M. Bardi, P. Caines, I. Dolcetta (2013)
Preface: DGAA Special Issue on Mean Field GamesDynamic Games and Applications, 3
-
Olivier Guéant, P. Lions, J. Lasry (2011)
Mean Field Games and Applications -
V. Kolokoltsov (2012)
Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions)International Journal of Statistics and Probability, 1
-
J. Lasry, P. Lions (2007)
Mean field gamesJapanese Journal of Mathematics, 2
-
V. Kolokoltsov, M. Troeva, Wei Yang (2014)
On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of PlayersDynamic Games and Applications, 4
-
D. Gomes, João Saúde (2014)
Mean Field Games Models—A Brief SurveyDynamic Games and Applications, 4
-
D. Bauso, H. Tembine, T. Başar (2016)
Robust Mean Field GamesDynamic Games and Applications, 6
-
D. Gomes, J. Mohr, Rafael Souza (2010)
Discrete Time, Finite State Space Mean Field GamesJournal de Mathématiques Pures et Appliquées, 93
-
Rani Basna, A. Hilbert, V. Kolokoltsov (2014)
An epsilon-Nash equilibrium for non-linear Markov games of mean-field-type on finite spaces, 8
-
Minyi Huang, P. Caines, R. Malhamé (2007)
Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash EquilibriaIEEE Transactions on Automatic Control, 52
- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by The Author(s)
- Subject
- Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-016-9389-6
- Publisher site
- See Article on Publisher Site
Abstract
We initiate the analysis of the response of computer owners to various offers of defence systems against a cyber-hacker (for instance, a botnet attack), as a stochastic game of a large number of interacting agents. We introduce a simple mean-field game that models their behavior. It takes into account both the random process of the propagation of the infection (controlled by the botner herder) and the decision making process of customers. Its stationary version turns out to be exactly solvable (but not at all trivial) under an additional natural assumption that the execution time of the decisions of the customers (say, switch on or out the defence system) is much faster that the infection rates.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Nov 9, 2016