Optimal Epidemics Policy Seeking on Networks-of-Networks Under Malicious Attacks by Geometric Programming

This work deals with the optimal epidemics policy-seeking problem on networks-of-networks (NoN) in the presence of unknown malicious adding-edge attacks. This problem is investigated in a framework of games-of-games (GoG), in which the conflicts between each network policymaker and the attacker are captured by a series of the Stackelberg games, while all network policymakers together compose a Nash game. First, the tolerable maximum attack magnitude is investigated and given implicitly. Then, we prove the existence of the gestalt Nash equilibrium (GNE) under mild attacks bounded by the above magnitude. A Heuristic algorithm based on iterative geometric programming is proposed to seek the GNE of the above GoG, whose asymptotical convergence is verified. Correspondingly, a greedy Heuristic strategy for the malicious attacker to compromise the NoN topology is developed. The practicability and validity of the above theoretical results and algorithms are illustrated via a simulation example.