This paper explored the theoretical and practical connections between topological data analysis (TDA), game theory, and data poisoning attacks. We demonstrated how the topological structure of data can influence strategic interactions in adversarial settings, and how game-theoretic frameworks can model the interplay between defenders and attackers in machine learning systems. We introduced novel formulations that bridge these fields, developing metrics to quantify the topological vulnerability of data structures to poisoning attacks. Our analysis reveals that persistence diagrams from TDA can serve as powerful tools for both detecting poisoning attempts and designing robust defense mechanisms. We proposed a Nash equilibrium-based approach to determine optimal poisoning and defense strategies, supported by mathematical formulations and theoretical guarantees.