In this paper, the problem of seeking optimal distributed resource allocation (DRA) policies on cellular networks in the presence of an unknown malicious adding-edge attacker is investigated. This problem is described as the games of games (GoG) model. Specifically, two subnetwork policymakers constitute a Nash game, while the confrontation between each subnetwork policymaker and the attacker is captured by a Stackelberg game. First, we show that the communication resource allocation of cellular networks based on the Foschini-Miljanic (FM) algorithm can be transformed into a \emph{geometric program} and be efficiently solved via convex optimization. Second, the upper limit of attack magnitude that can be tolerated by the network is calculated by the corresponding theory, and it is proved that the above geometric programming (GP) framework is solvable within the attack bound, that is, there exists a Gestalt Nash equilibrium (GNE) in our GoG. Third, a heuristic algorithm that iteratively uses GP is proposed to identify the optimal policy profiles of both subnetworks, for which asymptotic convergence is also confirmed. Fourth, a greedy heuristic adding-edge strategy is developed for the attacker to determine the set of the most vulnerable edges. Finally, simulation examples illustrate that the proposed theoretical results are robust and can achieve the GNE. It is verified that the transmission gains and interference gains of all channels are well tuned within a limited budget, despite the existence of malicious attacks.

翻译：本文研究了在存在未知恶意添加边攻击者的情况下，蜂窝网络中寻求最优分布式资源分配策略的问题。该问题被描述为博弈的博弈模型。具体而言，两个子网络决策者构成一个纳什博弈，而每个子网络决策者与攻击者之间的对抗则由斯塔克尔伯格博弈刻画。首先，我们证明基于Foschini-Miljanic算法的蜂窝网络通信资源分配可转化为几何规划问题，并通过凸优化高效求解。其次，利用相应理论计算网络所能容忍的攻击幅度上限，并证明上述几何规划框架在攻击界限内是可解的，即我们的博弈的博弈中存在格式塔纳什均衡。第三，提出一种迭代使用几何规划的启发式算法来识别两个子网络的最优策略剖面，同时验证了其渐近收敛性。第四，为攻击者开发了一种贪婪启发式添加边策略，以确定最脆弱边的集合。最后，仿真算例表明，所提出的理论结果具有鲁棒性，并能达到格式塔纳什均衡。验证了在恶意攻击存在的情况下，所有信道的传输增益和干扰增益均能在有限预算内得到良好调节。