  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.
