Sophisticated banking contracts and fragility when withdrawal information is public

Abstract

I study whether self‐fulfilling bank runs can occur when banks use sophisticated contracts and withdrawal decisions are public information. In a finite‐agent version of Diamond and Dybvig (1983) with correlated types, I first present an example in which a bank run perfect Bayesian equilibrium exists. However, its existence relies on off‐path beliefs that are unreasonable in terms of forward induction. To discipline beliefs, I use forward induction equilibrium (Cho (1987)) as the solution concept. I show that, whenever the allocation rule is strictly incentive compatible, the truth‐telling strategy is the unique forward induction equilibrium in the withdrawal game, and no bank run occurs. Therefore, with forward induction, sophisticated contracts can prevent bank runs when there is public information about withdrawal decisions.