In their seminal work on systemic risk in financial markets, Eisenberg and Noe proposed and studied a model with @math firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation -- if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of @math away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems.
We provide a framework to study the formation of financial networks and investigate the interplay between banks' lending incentives and the emergence of systemic risk. We show that under natural contracting assumptions, banks fail to internalize the implications of their lending decisions for the banks with whom they are not directly contracting, thus establishing the presence of a financial network externality in the process of network formation. We then illustrate how the presence of this externality can function as a channel for the emergence of systemic risk. In particular, we show that (i) banks may "overlend" in equilibrium, creating channels over which idiosyncratic shocks can translate into systemic crises via financial contagion; and (ii) they may not spread their lending sufficiently among the set of potential borrowers, creating insufficiently connected financial networks that are excessively prone to contagious defaults. Finally, we show that banks' private incentives may lead to the formation of financial networks that are overly susceptible to systemic meltdowns with some small probability. I develop a model of the financial sector in which endogenous intermediation among debt financed banks generates excessive systemic risk. Financial institutions have incentives to capture intermediation spreads through strategic borrowing and lending decisions. By doing so, they tilt the division of surplus along an intermediation chain in their favor, while at the same time reducing aggregate surplus. I show that a core-periphery network -- few highly interconnected and many sparsely connected banks -- endogenously emerges in my model. The network is inefficient relative to a constrained efficient benchmark since banks who make risky investments "overconnect", exposing themselves to excessive counterparty risk, while banks who mainly provide funding end up with too few connections. The predictions of the model are consistent with empirical evidence in the literature. We consider default by firms that are part of a single clearing mechanism. The obligations of all firms within the system are determined simultaneously in a fashion consistent with the priority of debt claims and the limited liability of equity. We first show, via a fixed-point argument, that there always exists a "clearing payment vector" that clears the obligations of the members of the clearing system; under mild regularity conditions, this clearing vector is unique. Next, we develop an algorithm that both clears the financial system in a computationally efficient fashion and provides information on the systemic risk faced by the individual system firms. Finally, we produce qualitative comparative statics for financial systems. These comparative statics imply that, in contrast to single-firm results, even unsystematic, nondissipative shocks to the system will lower the total value of the system and may lower the value of the equity of some of the individual system firms.