Persistence Game Theory: Strategy, Entropy, and the Collapse of Systems

This paper introduces Persistence Game Theory, a novel mathematical framework that reconceives strategy as a function not only of payoffs, but of a system’s capacity to survive under entropy. At its core is a persistence equation that models how reversibility, entropy pressure, systemic fragility, and thermodynamic slack jointly determine whether a game-like system continues to exist.In this framework, reversibility — the degree to which structural information is retained between states — becomes a strategic variable. Classical equilibria such as the Nash equilibrium are shown to be potentially unstable when they degrade system reversibility over time. We explore how strategic behaviour must adapt when agents operate within systems that can collapse, not only fail.Applications include cognitive fatigue, ecological overshoot, AI misalignment, and institutional decay. We introduce the concept of Persistence Landscapes to show how strategy spaces deform as reversibility is lost, leading to tipping points and entropic attractors. Persistence Game Theory thus offers a new grammar of strategy for systems that must not only win — but last.