A bank runs model with a continuum of types

We consider a bank runs model à la Diamond and Dybvig (1983) 3] with a continuum of agent types, indexed by the degree of patience. Much of our understanding based on the two-type model must be modified. The endogenous determination of a cutoff type is central to the analysis. In the case where the bank can credibly commit to a contract, the optimal contract results in socially excessive early withdrawals in every equilibrium of the post-deposit subgame. Thus, even at the best equilibrium the socially efficient outcome is not achieved, and agents? behavior exhibits features of a bank run. In the case where commitment is not possible, there are strictly more early withdrawals and strictly lower welfare than the full-commitment equilibrium.