On priority-proportional payments in financial networks

We study financial systems from a game-theoretic standpoint. A financial system is represented by a network, where nodes correspond to banks, and directed labeled edges correspond to debt contracts between them. The existence of cycles in the network indicates that a payment of a bank to one of its lenders might affect the bank's incoming payments. So, if a bank cannot fully repay its debt, then the exact payments it makes to each of its lenders can affect the cash inflow back to itself. We naturally assume that the banks are interested in their financial well-being (utility) which is aligned with the amount of incoming payments they receive from the network. This defines a game among the banks, that can be seen as utility-maximizing agents who strategize over their payments. We introduce a class of financial network games that arise under some natural payment strategies called priority-proportional payments. We compute valid payment profiles for fixed payment strategies and we investigate existence and (in)efficiency of equilibrium strategies, under different variations of the game that capture several financial aspects that commonly arise in practice. We conclude with examining the computational complexity of a variety of related problems.