Latent Fragility and Clustered Withdrawals in Dynamic Banks Runs

Using a mean-field game framework, we study a dynamic model of bank runs in which more withdrawals raise the risk of bank failure. Even though depositors receive gradual and idiosyncratic shocks, withdrawals occur in clusters. The main mechanism is latent fragility: run-prone depositors accumulate gradually over time and may prefer to wait individually, but they withdraw together once collective exit becomes self-fulfilling. We establish equilibrium existence and characterize earliest-run and latest-run equilibria. The clustering mechanism arises whether depositor heterogeneity is discrete or continuous. A common aggregate state coordinates withdrawal timing and leads to a unique threshold equilibrium.