Optimal Resource Allocation Between Two Nonfully Cooperative Wireless Networks Under Malicious Attacks: A Gestalt Game Perspective

This work studies the problem of finding optimal distributed resource allocation policies on wireless networks in the existence of an unknown malicious adding-edge attacker, depicted as the games of games (GoG) model. Specifically, two subnetwork policymakers constitute a Nash game, while a Stackelberg game captures the confrontation between each subnetwork policymaker and the malicious attacker. We first demonstrate that by utilizing the Foschini-Miljanic algorithm, the communication resource allocation of cellular networks can be converted into a geometric program (GP) that can be efficiently solved by convex optimization. Then, the upper limit of attack magnitude that the network can withstand is calculated. It is shown that the proposed GP framework is solvable within the attack bound and a Gestalt Nash equilibrium (GNE) exists for the GoG. Moreover, a heuristic algorithm that iteratively employs GP is developed to obtain the optimal policy profiles of subnetworks, which can converge asymptotically. Correspondingly, a greedy heuristic adding-edge strategy is proposed to identify the set of the most vulnerable edges for the attacker. Finally, simulation examples show that the obtained algorithm is resilient to malicious attacks and can attain the GNE. Despite the presence of malicious attacks, all channels’ transmission and interference gains can be well-adjusted within a limited budget.