Combined Evolutionary and Mean-Field Setting for the Pressure- Resistance Games on Networks

Stamatios Katsikas
University of Warwick

The recently developed mean-field-game models of corruption [2] and botnet defense in cyber-security [3], along with the evolutionary game approach of inspection and corruption [4], can be combined under an extended setting including the pressure and resistance game element [1]. We propose here a general framework for interaction in networks that includes binary interaction (the evolutionary game component), individual decision making inside the environment (the mean-field game component), the action of the principal or the major player (the pressure-resistance game component), and the noise. In order to perform concrete calculations with this overall complicated model,
we suggest working in three asymptotic regimes; fast execution of personal decisions, small rates of binary interactions, and strong discounting in time.

[1] Kolokoltsov, V. (2014). The evolutionary game of pressure (or interference), resistance and collaboration. arXiv preprint arXiv:1412.1269.
[2] Kolokoltsov, V. N., & Malafeyev, O. A. (2015). Mean-field-game model of corruption. arXiv preprint arXiv:1507.03240.
[3] Kolokoltsov, V. N., & Bensoussan, A. (2016). Mean-field-game model for Botnet defense in Cyber-security. Applied Mathematics & Optimization, 74(3), 669-692.
[4] Katsikas, S., Kolokoltsov, V., & Yang, W. (2016). Evolutionary Inspection and Corruption Games. Games, 7(4), 31.

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