The Inertia of Norms: A Sigmoidal Synthesis of Evolutionary Game Theory and Cultural Lag

Background: A fundamental tension exists between Rational Choice Theory (which predicts rapid optimization) and Sociological Theory (which predicts inertia and lag). Standard Evolutionary Game Theory models adoption as a linear function of utility, failing to account for ”Threshold Behavior” observed in social change. Method: We perform a formal synthesis of the standard Replicator Dynamic Equation and the Time-Dependent Agency model proposed by Da˘g (2026). By scaling the micro-level ontogenetic parameters to the macro-level, we derive a ”Sigmoidal Inertia Equation.” Results: We demonstrate that cultural plasticity is not linear but logistic. The adoption of a new norm requires the utility gap (∆π) to exceed a specific ”Social Activation Energy.” Conclusion: This framework mathematically resolves four historical anomalies: Ogburn’s Cultural Lag, Granovetter’s Tipping Points, Pluralistic Ignorance, and Institutional Path Dependence.