Epidemic Protection Over Heterogeneous Networks Using Evolutionary Poisson Games

Malware is increasingly sophisticated and affects the wellbeing of a large population of heterogeneous and highly connected devices. The users of these devices can make strategic and dynamic decisions to choose whether or not to adopt the antivirus software, not only to secure their individual devices but also to protect the network they are part of. Motivated by the strategic behaviors of the antivirus adoption, we establish an evolutionary Poisson game framework to capture the random, dynamic, and heterogeneous interactions of agents in a holistic fashion, and design mechanisms to control their behaviors to achieve a system-wide objective. We first prove the existence and uniqueness of a mixed Nash equilibrium of the large population game and show that the equilibrium is an evolutionary stable strategy. Finally, we develop online algorithms using the techniques of stochastic approximation coupled with the population dynamics, and they are shown to converge to the optimal solution of the controller problem. Numerical examples are used to illustrate and corroborate our results.