Quantized distributed Nash equilibrium seeking under DoS attacks

Abstract

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.