Cloud computing, a transformative paradigm, has ushered in an era of unparalleled convenience and economic efficiency for both service providers and users. Historically, before its widespread adoption, digital services were susceptible to Distributed Denial of Service (DDoS) attacks, which aimed to overwhelm server capacities. The advent of cloud computing has primarily mitigated these threats but, in doing so, has inadvertently introduced new vulnerabilities. In their relentless pursuit of exploitation, attackers have transitioned from targeting server performance to inflicting economic damages. A particularly insidious form of this is the Yo-Yo Attack, an Economic Denial of Sustainability (EDoS) strategy that manipulates the auto-scaling features inherent to cloud systems. This thesis presents a novel mathematical framework to understand the ongoing tussle between cloud service providers and Yo-Yo Attackers. We conceptualize this conflict as a Repeated Dynamic Bayesian Stackelberg game. This approach is pioneering in capturing the Yo-Yo attacker's nuanced strategies, particularly their adeptness at exploiting the cloud's auto-scaling features. The Learning-Based Attackers’ Type Recognition and Defense Mechanism is central to our game model, which harnesses the power of one-class Support Vector Machine (SVM) to discern the modus operandi of various Yo-Yo attack types. Our research further introduces an innovative machine-learning algorithm adept at recognizing and countering the unique attack patterns of individual bots. We delve deeper into a proposed defense mechanism, which recognizes different strategies of Yo-Yo attackers aiming to exploit different vulnerabilities of the cloud’s auto-scaling mechanism and thereby confound their efforts. Our empirical experiments underscore the efficacy of our solution. Our approach demonstrates superior reduced compromised services and overall efficiency compared to existing Yo-Yo detection and defense strategies. In conclusion, as cloud computing continues to dominate the digital landscape, ensuring its security remains paramount. Our research offers a robust solution to a new generation of threats, setting a benchmark for future endeavors in cloud security.