Quantized distributed Nash equilibrium seeking under DoS attacks

TL;DR

This paper introduces a resilient quantized distributed Nash equilibrium seeking method that withstands DoS attacks and quantization constraints, ensuring convergence and robustness in adversarial network environments.

Contribution

It proposes a novel quantized NE seeking strategy with zooming-in and holding capabilities, providing conditions to prevent quantizer saturation under DoS attacks.

Findings

The strategy achieves maximum resilience to DoS attacks.

Quantizer saturation can be avoided with sufficient levels.

The method ensures convergence despite malicious disruptions.

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.