Sophisticated Banking Contracts and Fragility When Withdrawal Information is Public
Accepted at Theoretical Economics
49 Pages Posted: 13 Jul 2021 Last revised: 11 Jan 2023
Date Written: July 11, 2021
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 these 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 banking contracts can eliminate banking fragility when there is public information about withdrawal decisions.
Keywords: Bank runs; Sophisticated contracts; Public information; Forward induction; Correlated types.
JEL Classification: D82, D83, G21
Suggested Citation: Suggested Citation