Strategic Equilibrium in Topological Games: Historical Development, Theoretical Challenges, and Interdisciplinary Reflections

This paper investigates the historical evolution, theoretical limitations, and interdisciplinary applications of strategic equilibrium through the lens of topological game theory. Departing from classical models based on finite strategy sets and continuous utility functions, it explores how convexity, continuity, and tightness determine the viability of equilibrium in more complex, infinite, or discontinuous environments. The study revisits foundational results from von Neumann, Kakutani, and Nash, while extending their implications into non-classical strategic landscapes. Beyond its theoretical framework, the paper offers an original contribution by embedding topological game theory into the analysis of two major historical transformations: the Industrial Revolution and the Cold War. These episodes are conceptualized as disruptions in the topology of strategic interaction featuring non-convex preferences, abrupt shifts, and fragile equilibria. The Industrial Revolution restructured socio-spatial strategy sets through technological upheaval, while Cold War deterrence evolved within a symbolically mediated and discontinuous geopolitical topology. This is the first systematic attempt to integrate topological game theory with the historical analysis of strategic behavior. The paper demonstrates how topological reasoning can uncover the hidden architecture of conflict, extend fixed-point logic beyond classical confines, and enhance our understanding of strategic complexity in disciplines such as economics, political science, and network theory.