Psychological Lock-In and Institutional Persistence: A Mean-Field Model of Confidence Dynamics

We establish a mean-field stochastic framework for analyzing institutional lock-in driven by asymmetric belief updating. A continuum of agents update confidence levels s_tthrough success/failure experiences, with update functions F_S,F_Fexhibiting negativity bias: failures impact beliefs more strongly than successes of equal magnitude. Aggregate confidence I_tinfluences the success probability \pi(I_t), creating feedback between individual psychology and collective outcomes. We prove existence of stationary equilibria via Schauder’s fixed-point theorem on the space of probability measures \mathcal{P}\left(\left[0,1\right]\right), establishing compactness through Prokhorov’s theorem. Stability is characterized via spectral analysis of Fréchet derivatives in the bounded-Lipschitz metric, with operator decomposition into push-forward L_{\mu^\ast} and rank-one feedback R_{\mu^\ast} components. Under negativity bias and positive feedback, we establish multiplicity: generically three equilibria (low, middle, high) with stable-unstable-stable pattern. For escape dynamics from stable equilibria, we establish a large deviation principle on Skorokhod space D\left([0,\infty\right),\mathcal{P}\left(\left[0,1\right]\right)) with rate function determined by a quasi-potential computed via action functional minimization. Expected escape times scale as exp\left(N\cdot V\right) where N is population size and V is the quasi-potential, confirming exponential rarity: for calibrated parameters with N={10}^6 agents, escape times exceed {10}^{63,900} periods. We derive comparative statics for reform policy through optimal control: value function concavity implies optimal sequencing places high-success-probability reforms first. Material investments M and psychological interventions P exhibit strategic complementarity (\partial^2I^\ast/\partial M\partial P>0), verified through implicit function theorem analysis. Numerical verification with {10}^6 Monte Carlo simulations confirms all theoretical predictions, with robustness checks across alternative functional specifications. The framework provides a rigorous foundation for understanding institutional persistence as emerging from collective psychological dynamics rather than material coordination failures, with implications for development economics, political economy, and organizational change.