Coordination failures, bank runs and asset prices

We study efficiency properties of competitive economies in which banks provide liquidity insurance and interact on secondary asset markets. While all banks are subject to extrinsic risk, a bank's portfolio choice determines whether it is prone to a bank run in one of the extrinsic states. Asset prices determine the value of bank assets and thus how to structure run-proof portfolios. Except for very large sunspot probabilities, equilibria with trivial sunspots exist, where asset prices are state-dependent, bank runs do not occur and the efficient allocation obtains. Interbank asset markets are also a new source of multiplicity of equilibrium. For low sunspot probabilities, there are equilibria in which all banks are run-prone. For high sunspot probabilities, there is no equilibrium with run-prone banks but consumption can be indeterminate. If the sunspot probability is neither high nor low, equilibria may exist in which some banks are run-prone and others are run-proof.