Bank Runs: Regulation Vs. Coordination Problem

This paper employs game theory to provide insights into the phenomenon of bank runs. The model presented in the study involves each player making a decision between withdrawing their deposit from the bank, thereby forfeiting accumulated interest, or leaving the deposit in the bank, which involves the risk of partial or total loss. The model incorporates variables such as interest rates, transaction fees, stock falls rate, and deposit insurance to reflect real-world conditions. The primary aim of this contribution is to analyze the fundamental causes of bank runs and evaluate the effects of deposit insurance on depositors' withdrawal strategies. Within the framework of a dynamic game with incomplete information, a payoff matrix is constructed for the players, and the results are thoroughly examined. The analysis reveals two Bayesian Nash equilibria and identifies two strategies that are considered optimal in the context of the game without deposit insurance. In this scenario, these strategies lead to the occurrence of a bank run. Conversely, when deposit insurance is introduced into the game, the optimal strategy shifts to keeping deposits in the bank. This adjustment reduces the likelihood of bank runs, highlighting the stabilizing effect of deposit insurance on the banking system. Nevertheless, the article shows with examples, that the deposit insurance is not such effective as it is thought and that the bank run is a coordination problem rather than regulation, while the macroprudential policy plays a significant role in the depositor’s behavior.