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.
Assessing the Likelihood of Panic-Based Bank Runs