Equity Consistency in Financial Networks

This paper considers financial networks for which the population of agents can vary and where network clearing occurs under limited liability, absolute priority, and general agent-specific division rules. After clearing the network, each agent's equity is determined by its initial assets plus the difference between what it received and paid. We introduce reduced financial networks to study how the equity of agents changes when some agents exit. We define equity consistency as the principle that no subset of agents should have an incentive to break away and revise the initial equity assigned to them. We show that equity consistency is achieved if and only if the division rules used for clearing are consistent. For instance, the proportional rule and priority rules are consistent. Nevertheless, one should be careful when using a decentralized procedure to clear the network. Even with consistent division rules, agents' equities may change if they decide to break away. Interestingly, although clearing in accordance with consistent division rules ensures consistent equity to the agents, we demonstrate that the underlying clearing payments are not always consistent.