A network centrality game based on a compact representation of defender's belief for epidemic control

. The mathematical theory of epidemics draws upon essential concepts from epidemiology, categorizing the population into three distinct compartments: Susceptible, Infected, and Resistant individuals. This battle between a malicious, intelligent, and rational agent disseminating the threat and a defender attempting to restrict its propagation is generally modeled by a partially observable stochastic game (POSG). Despite its broad applicability, solving this game is still not feasible due to the size of the state space and thus the complexity of updating the defender's belief at each step. To circumvent this "curse of dimensionality", we present a novel framework that takes into account the network topology through centrality measures. We demonstrate that the defender, instead of updating his belief concerning the state of the network, can apply a condensed representation of his belief regarding the state of each node at each step, without changing his optimal strategy. The defender manages a vector of size n (in a network with n nodes) instead of a vector of size 2(n). Numerical illustrations demonstrate that using the condensed representation of the defender's belief enhances the scalability and reduces the convergence time of the algorithm.