Competition over Epidemic Networks: Nash and Stackelberg Games

We study the competition over epidemic networks within a game-theoretic framework. Based on the homogeneous n-intertwined Markov model for epidemic spread, we introduce a novel epidemic competition between a network designer and an intelligent adversary, where the designer can protect the network by increasing the curing rate and the adversary, on the contrary, is able to manipulate the infection rate in order to do as much damage as possible. We focus on the case where the underlying graph is fully connected but the analysis can be readily extended to the case of the connected k-regular graph. We fully characterize the Nash solutions and Stackelberg solutions when either the designer or the adversary is the leader, and show that how each player will play in the games will largely depend on the relative costs for protecting and attacking the network.