<p>The distributed denial-of-service (DDoS) attack targeting edge servers (ESs), also known as the edge DDoS (EDDoS) attack, is a type of severe threat in edge computing. Recently, end-edge-cloud computing has been proposed to absorb EDDoS traffic. In this field, this paper addresses the cloud assistance (CA) problem, which is to determine the cloud assistance rates of ESs so that the total task latency is minimized, on the condition that the task producing rates of malicious user endpoints are strategically controlled by the attacker. First, a system load dynamics model is proposed, and the CA problem is reduced to a differential game model under Nash equilibrium (NE). Second, necessary conditions of NEs are derived. Through applying the shooting method and grey wolf (GW) algorithm, the CA algorithm, which aims to find a possible NE from necessary conditions, is presented. Third, through numerical experiments, the optimal configuration, performance, and scalability of the CA algorithm are investigated, and the sensitivity of NEs is explored. Results show that the CA algorithm can yield a potential NE with a low error, that the GW algorithm can achieve similar performance with popular meta-heuristic methods but much higher performance than gradient-based methods, and that the potential NE is likely to be a real NE.</p>