Game-Theoretic Protection Adoption Against Networked SIS Epidemics

In this paper, we investigate game-theoretic strategies for containing spreading processes on large-scale networks. Specifically, we consider the class of networked susceptible-infected-susceptible (SIS) epidemics where a large population of agents strategically choose whether to adopt partially effective protection. We define the utilities of the agents which depend on the degree of the agent, its individual infection status and action, as well as the the overall prevalence of the epidemic and strategy profile of the entire population. We further present the coupled dynamics of epidemic evolution as well as strategy update which is assumed to follow the replicator dynamics. By relying on timescale separation arguments, we first derive the game-theoretic protection adoption strategies of the agents for a given epidemic state, and then present the reduced epidemic dynamics. The existence and uniqueness of endemic equilibrium is rigorously characterized and forms the main result of this paper. We then present extensive numerical results to highlight the impacts of heterogeneous node degrees, infection rates, cost of protection adoption, and effectiveness of protection on the epidemic prevalence at the equilibrium. Finally, we illustrate the evolution of the networked SIR epidemic under game-theoretic protection adoption.