Commitment and equilibrium bank runs

We study the role of commitment in a version of the Diamond-Dybvig model with no aggregate uncertainty. As is well known, the banking authority can eliminate the possibility of a bank run by committing to suspend payments to depositors if a run were to start. We show, however, that in an environment without commitment, the banking authority will choose to only partially suspend payments during a run. In some cases, the reduction in early payouts under this partial suspension is insufficient to dissuade depositors from participating in the run. Bank runs can then occur with positive probability in equilibrium. The fraction of depositors participating in such a run is stochastic and can be arbitrarily close to one.