We answer the following question: Does regulating the banking network increase systemic risk in the entire financial network in the presence of unregulated shadow banks? In order to answer this question, we introduce a formal definition of systemic risk based on the equilibrium state dynamics generated by a stochastic game of network formation with banks and shadow banks. Based on the equilibrium dynamics, we discuss the properties of equilibrium financial networks. The predictions of the model are consistent with empirical evidence in the literature. Our analysis makes clear the systemic importance of connections between commercial banks and shadow banks in determining the health of the entire financial network. Lastly, but most importantly, we give a definition of systemic risk based on equilibrium dynamics, and therefore, a definition which takes into account the strategic interactions of financial institutions when facing different regulatory policies. Given our definition of systemic risk, we discuss various policies for regulating the financial system. Then, specializing our dynamic stochastic game model to a more basic model in which banks and shadow banks form a network including connections to the real economy, we show, via numerical simulations of our stochastic game model under various regulatory regimes, that imposing bank regulations not faced by shadow banks does indeed increase systemic risk throughout the financial network.
