Forgiving Debt in Financial Network Games

We consider financial networks, where nodes correspond to banks and directed labeled edges correspond to debt contracts between banks. Maximizing systemic liquidity, i.e., the total money flow, is a natural objective of any financial authority. In particular, the financial authority may offer bailout money to some bank(s) or forgive the debts of others in order to maximize liquidity, and we examine efficient ways to achieve this. We study the computational hardness of finding the optimal debt-removal and budget-constrained optimal bailout policy, respectively, and we investigate the approximation ratio provided by the greedy bailout policy compared to the optimal one. We also study financial systems from a game-theoretic standpoint. We observe that the removal of some incoming debt might be in the best interest of a bank. Assuming that a bank's well-being (i.e., utility) is aligned with the incoming payments they receive from the network, we define and analyze a game among banks who want to maximize their utility by strategically giving up some incoming payments. In addition, we extend the previous game by considering bailout payments. After formally defining the above games, we prove results about the existence and quality of pure Nash equilibria, as well as the computational complexity of finding such equilibria.