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.
To our knowledge, strategic aspects are currently reflected only in models of network formation @cite_10 @cite_9 . A three period economy is assumed where firms can invest into risky assets. To do so, they strategically decide to borrow funds from outside investors as well as other firms. Thereby a network of financial cross-holdings is endogenously formed as each firm maximizes their expected profit. The results show that risk-seeking firms tend to over-connect leading to stronger contagion and systemic risk as compared to the socially optimal risk-sharing allocation. Note that in this case, strategic aspects only play a role in the formation of inter-bank relations whereas the clearing mechanism is assumed to follow the same process as in @cite_3 .
@cite_9 @cite_10 @cite_3
100186914 2160164079 2013403206 2103720435
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 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. We propose a simple model of inter-bank borrowing and lending where the evolution of the log-monetary reserves of @math banks is described by a system of diffusion processes coupled through their drifts in such a way that stability of the system depends on the rate of inter-bank borrowing and lending. Systemic risk is characterized by a large number of banks reaching a default threshold by a given time horizon. Our model incorporates a game feature where each bank controls its rate of borrowing lending to a central bank. The optimization reflects the desire of each bank to borrow from the central bank when its monetary reserve falls below a critical level or lend if it rises above this critical level which is chosen here as the average monetary reserve. Borrowing from or lending to the central bank is also subject to a quadratic cost at a rate which can be fixed by the regulator. We solve explicitly for Nash equilibria with finitely many players, and we show that in this model the central bank acts as a clearing house, adding liquidity to the system without affecting its systemic risk. We also study the corresponding Mean Field Game in the limit of large number of banks in the presence of a common noise. This paper presents the first study of the endogenous formation of networks by strategic, self-interested agents who benefit from producing and disseminating information. This work departs from previous works on network formation (especially in the economics literature) which assume that agents benefit only by acquiring information produced by other agents. The strategic production and dissemination of information have striking consequences. We show first that the network structure that emerges (in equilibrium) typically displays a core-periphery structure, with the few agents at the core playing the role of eeconnectorsee, creating and maintaining links to the agents at the periphery. We then determine conditions under which the networks that emerge are minimally connected and have short network diameters (properties that are important for efficiency). Finally, we show that the number of agents who produce information and the total amount of information produced in the network grow at the same rate as the agent population; this is in stark contrast to the "law of the few" that had been established in previous works which do not consider information dissemination.