Strategic Interplay: Game-Theoretic Frameworks for Topological Robustness Against Data Poisoning

This investigation explores the strategic dynamics between adversarial manipulation and defensive mechanisms through the lens of game theory and topological data analysis. We construct a novel theoretical framework that synthesizes concepts from cooperative game theory with the structural insights provided by persistence homology to formulate defensive strategies against data poisoning attacks. Our central contribution is a gametheoretic equilibrium model that characterizes the competitive interaction between attackers attempting to compromise data integrity and defenders working to preserve topological invariants. We introduce the concept of topological resilience coefficient as a measure of structural vulnerability, supported by a novel theorem establishing bounds on attack effectiveness under equilibrium conditions. Experimental validation demonstrates that our approach yields significantly improved robustness against sophisticated poisoning strategies when compared to conventional defenses. The presented framework offers both theoretical foundations and practical methodologies for designing systems resistant to adversarial manipulation while preserving essential structural characteristics in machine learning applications.