Social Contagion and Bank Runs: An Agent-Based Model with LLM Depositors

Digital banking and online communication have made modern bank runs faster and more networked than the canonical queue-at-the-branch setting. While equilibrium models explain why strategic complementarities generate run risk, they offer limited guidance on how beliefs synchronize and propagate in real time. We develop a process-based agent-based model that makes the information and coordination layer explicit. Banks follow cash-first withdrawal processing with discounted fire-sale liquidation and an endogenous stress index. Depositors are heterogeneous in risk tolerance and in the weight placed on fundamentals versus social information, communicating on a heavy-tailed network calibrated to Twitter activity during March 2023. Depositor behavior is generated by a constrained large language model that maps each agent's information set into a discrete action and an optional post; we validate this policy against laboratory coordination evidence and theoretical benchmarks. Across 4,900 configurations and full LLM simulations, three findings emerge. Within-bank connectivity raises the likelihood and speed of withdrawal cascades holding fundamentals fixed. Cross-bank contagion exhibits a sharp phase transition near spillover rates of 0.10. Depositor overlap and network amplification interact nonlinearly, so channels weak in isolation become powerful in combination. In an SVB, First Republic, and regional bank scenario disciplined by crisis-era data, the model reproduces the observed ordering of failures and predicts substantially higher withdrawal rates among uninsured depositors. The results frame social correlation as a measurable amplifier of run risk alongside balance-sheet fundamentals.