Quantized distributed Nash equilibrium seeking under DoS attacks: A quantized consensus based approach

2023-08-24

arXiv.org

AI Summary

This paper addresses the robust distributed Nash equilibrium (NE) seeking problem under concurrent communication constraints and malicious Denial-of-Service (DoS) attacks. To handle quantized inter-agent information exchange, stochastic packet drops, and DoS-induced communication interruptions, we propose a novel dynamic quantization mechanism with scaling-and-holding capability, achieving— for the first time—the theoretically maximal DoS resilience guarantee. We further design an anti-saturation quantization strategy and derive a sufficient condition on the minimum number of quantization levels to prevent quantizer saturation. By integrating dynamic quantized consensus with distributed gradient tracking, we rigorously prove that the algorithm converges to the NE even under worst-case DoS attacks and packet losses. Our main contributions lie in breaking the convergence analysis bottleneck under joint quantization and DoS constraints, thereby enabling a synergistic optimization of resilience, solution accuracy, and communication efficiency.

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.

Problem

• Nash Equilibrium
• Distributed Strategies
• Consensus under Attack

Innovation

• Nash Equilibrium
• Signal Amplification and Holding
• Threshold Condition for Unattainability