This paper presents an approach to understand the bank runs with game theory. In the model, each player decides if they withdraw their deposit from the bank and loose accumulated interest or leave the deposit in the bank risking losing the deposit partially or completely. The model considers interest rates, transaction fees, and deposit insurance. The aim of the contribution is to analyse the root cause of bank runs and investigate the impact of deposit insurance on the depositors’ withdrawal strategies. Within a dynamic game with incomplete information, a playoff matrix for players is build and the results are analyzed. The results show that there two Bayesian Nash equilibrium and two strategies that can be considered as optimal in the game without deposit insurance which leads to a bank run. On the other hand, with deposit insurance introduced in the game, the optimal strategy is to keep the deposits in the bank which minimizes probability of bank runs.