Strategic default and optimal audit resources with costly state verification

I develop a model in which the ability to repay a loan is private information that can only be verified by the bank at some costs, which can be recovered from the borrower if it has reported untruthfully. The bank will optimize the resources it spends on this auditing of borrowers and the resulting equilibrium is then characterized. It is shown that in equilibrium, a significant fraction of companies default strategically, but most are captured via auditing. The failure rates of banks are also small. Finally extensions are discussed to include limited liability to banks and the partial recovery of auditing costs as well as punitive costs to borrowers.