Strategic Behavior and Endogenous Risk of Contagion in a Financial Network: A Network Formation Game

This paper attempts to analyze the endogenous risk of contagion within an interbank network resulting from an external shock hitting the system. It uses a network formation game theoretic model to investigate the strategic interactions that may be observed once the shock has entered the network and thus endogenized itself. The primary results of this model indicate that the marginal utility that banks derive out of being in the network or alternatively, initiating connections to neighboring banks is negatively related to their degree of centrality as well as exposure levels. As such, their optimal strategy seems to be one that balances the level of their centrality and exposure, which in turn is a measure of their risk of contagion. Moreover, it is found that if a subnetwork of banks is highly connected then, with a very high probability, it is likely that it will entirely collapse. It is shown that there exists a stationary probability distribution that ensures this.