# American Institute of Mathematical Sciences

October  2019, 6(4): 315-335. doi: 10.3934/jdg.2019021

## Evolutionary, mean-field and pressure-resistance game modelling of networks security

 1 Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL, UK 2 Department of Statistics, University of Warwick, Associate Member of IPI RAN, Coventry, CV4 7AL, UK

Received  August 2019 Revised  August 2019 Published  October 2019

The recently developed mean-field game models of corruption and bot-net defence in cyber-security, the evolutionary game approach to inspection and corruption, and the pressure-resistance game element, can be combined under an extended model of interaction of large number of indistinguishable small players against a major player, with focus on the study of security and crime prevention. In this paper we introduce such a general framework for complex interaction in network structures of many players, that incorporates individual decision making inside the environment (the mean-field game component), binary interaction (the evolutionary game component), and the interference of a principal player (the pressure-resistance game component). To perform concrete calculations with this overall complicated model, we suggest working, in sequence, in three basic asymptotic regimes; fast execution of personal decisions, small rates of binary interactions, and small payoff discounting in time.

Citation: Stamatios Katsikas, Vassilli Kolokoltsov. Evolutionary, mean-field and pressure-resistance game modelling of networks security. Journal of Dynamics & Games, 2019, 6 (4) : 315-335. doi: 10.3934/jdg.2019021
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The simplified version of our network: only transitions between neighbours are allowed in $H$, all transitions are allowed in $B$, binary interaction occurs only within a common level in $H$
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