Assessing the Likelihood of Panic-Based Bank Runs

Conditional on the considered equilibrium, the probability of a bank run in the demand-deposit contract models of Bryant (1980) and of Diamond and Dybvig (1983) is either one or zero. In contrast, we establish the existence of an interval - being a strict subset of the unit-interval - of possible bank run probabilities for a two-player demand-deposit contract model where players receive independent signals about their liquidity desire from a continuous type space. As our main result we demonstrate that this interval reduces to a unique probability of a panic-based bank strictly smaller than one if and only if there exist types for which not running on the bank is a dominant action. In addition to existing models of bank runs such as, e.g., Goldstein and Pauzner (2005), our approach also provides some assessment of the likelihood of a bank run if there are no types for which not running on the bank is a dominant action. As a consequence, we can investigate the comparative statics of the likelihood of bank runs with respect to a larger range of payoff parameters than considered in previous models. Furthermore, we derive a technical result by which the findings of Morris and Shin (2005) on the dominance-solvability of binary action games with strategic complements also apply to nice games in the sense of Moulin (1984) if players' best response functions are increasing.