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Title: Mean-field-game model for Botnet defense in cyber-security
Authors: Kolokoltsov, VN
Bensoussan, A
Keywords: Botnet defence
Mean-field game
Phase transitions
Stable equilibrium
Issue Date: 2016
Publisher: Springer
Source: Applied mathematics and optimization, 2016, v. 74, no. 3, p. 669-692 How to cite?
Journal: Applied mathematics and optimization 
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.
ISSN: 0095-4616
EISSN: 1432-0606
DOI: 10.1007/s00245-016-9389-6
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