Epistemic Evolutionary Stability: When Belief Dynamics Reshape the Landscape of Cooperation

This deposit contains the paper and companion replication notebook for "Epistemic Evolutionary Stability: When Belief Dynamics Reshape the Landscape of Cooperation." The paper studies evolutionary stability when agents are uncertain about the operative payoff frame and revise beliefs through experience. It defines epistemic games, epistemic fixed points, and epistemic evolutionary stability relative to a class of belief-dependent strategies, then proves four results. First, under a uniform negative-drift condition, an all-defect certainty trap is an epistemic ESS: it absorbs mutants with arbitrary initial beliefs, including initially correct beliefs. Second, on graphs, cooperation resists frame-manipulator invasion exactly when rewiring outruns infection, and this resistance upgrades to epistemic ESS under an explicit post-isolation repair rule. Third, in finite populations a hard epistemic deadline governs cooperative fixation: a rare cooperative mutant must escape the negative-drift region before its belief leaves the cooperation basin, yielding a population-size/learning-rate crossover with no classical analogue. Fourth, in a coordination-game extension, the classical 1/3 rule shifts against cooperation by an explicit epistemic penalty. Every result collapses to its standard counterpart when the leverage parameter λ is set to zero and beliefs are fixed, establishing complete backward compatibility with classical ESS theory. The companion Colab notebook (Python; numpy, networkx, matplotlib) reproduces all numerical illustrations: Theorem 1 validation via epistemic Moran process simulation, Assumption 1 drift-margin verification, graph rewiring dynamics against frame-manipulator invasion, finite-population deadline and crossover curves, and the epistemic 1/3 rule shift under Stag-Hunt coordination. The notebook is self-contained with no proprietary dependencies.