A financial system is represented by a network, where nodes correspond to banks, and directed labeled edges correspond to debt contracts between banks. Once a payment schedule has been defined, where we assume that a bank cannot refuse a payment towards one of its lenders if it has sufficient funds, the liquidity of the system is defined as the sum of total payments made in the network. Maximizing systemic liquidity is a natural objective of any financial authority, so, we study the setting where the financial authority offers bailout money to some bank(s) or forgives the debts of others in order to maximize liquidity, and examine efficient ways to achieve this. We investigate the approximation ratio provided by the greedy bailout policy compared to the optimal one, and we study the computational hardness of finding the optimal debt-removal and budget-constrained optimal bailout policy, respectively. 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, if that helps one of its borrowers remain solvent and avoid costs related to default. 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.
翻译:金融系统由网络代表,网络的节点与银行相对应,而定向标签游戏则与银行之间的债务合同相对应。一旦确定了付款时间表,我们假设银行如果资金充足,不能拒绝向一个放款人付款,那么该系统的流动资金就被定义为网络中支付总额的总和。尽量扩大系统性流动性是任何金融当局的自然目标,因此,我们研究金融当局向某些银行提供救助资金或免除其他银行债务以便最大限度地提高流动性的稳定性的架构,并研究实现这一目标的有效方法。我们调查贪婪的拯救政策所提供的接近比率,与最佳政策相比,我们假设银行的贪婪拯救政策所提供的近似比率,我们研究找到最佳债务减免和预算限制的最佳拯救政策的计算难度。我们还从游戏理论角度研究金融体系。我们发现,取消某些债务可能符合银行的最佳利益,如果这有助于其借款人保持偿债能力,并避免与违约相关的成本。假设银行的幸福率(即)由贪婪的拯救政策提供的接近率与最优性保值政策相比,我们研究了找到最佳的取消债务和预算约束的最佳保值政策。我们从前的支付方式来定义了银行的支付方式,我们如何界定了银行的支付方式,从而从稳定地界定了清算的支付。我们从交易中推算中推算。