This paper studies distributed Nash equilibrium (NE) seeking under Denial-of-Service (DoS) attacks and quantization. The players can only exchange information with their own direct neighbors. The transmitted information is subject to quantization and packet losses induced by malicious DoS attacks. We propose a quantized distributed NE seeking strategy based on the approach of dynamic quantized consensus. To solve the quantizer saturation problem caused by DoS attacks, the quantization mechanism is equipped to have zooming-in and holding capabilities, in which the holding capability is consistent with the results in quantized consensus under DoS. A sufficient condition on the number of quantizer levels is provided, under which the quantizers are free from saturation under DoS attacks. The proposed distributed quantized NE seeking strategy is shown to have the so-called maximum resilience to DoS attacks. Namely, if the bound characterizing the maximum resilience is violated, an attacker can deny all the transmissions and hence distributed NE seeking is impossible.

翻译：本文研究在拒绝服务（DoS）攻击和量化条件下的分布式纳什均衡（NE）寻求问题。参与者仅能与直接邻居交换信息，且传输信息受量化以及恶意DoS攻击引发的数据包丢失影响。我们提出一种基于动态量化一致性方法的量化分布式NE寻求策略。为解决DoS攻击导致的量化器饱和问题，所设计的量化机制具备缩放与保持功能，其中保持能力与DoS攻击下量化一致性的相关结论一致。本文给出了量化器层数的充分条件，确保量化器在DoS攻击下不会饱和。所提出的分布式量化NE寻求策略具有对DoS攻击的最大鲁棒性。换言之，若刻画最大鲁棒性的边界条件被违反，攻击者可阻断所有传输，此时分布式NE寻求将无法实现。