On the resolution of cross-liabilities

In a variety of systems, in particular in a financial system, entities hold liabilities on each other. The reimbursement abilities are intertwined, thereby potentially generating coordination failures and cascades of defaults calling for orderly resolution. With a single indebted firm, a bankruptcy law organizes such an orderly resolution. With cross-liabilities, a resolution rule should be defined at the system level to account for all those affected, directly or indirectly. This paper investigates such rules assuming their primary goal is to avoid defaults on creditors external to the system, say banks' defaults on customers' deposits. I define and characterize the constrained-proportional rule building on two approaches: the minimization of an inequality measure on the reimbursements (made and received) and the axiomatization through desirable properties.