This paper has two main objectives: first, to provide a formal definition of endogenous systemic risk that is firmly grounded in equilibrium dynamics of temporary financial networks (i.e., short-term lending and investment networks); and second, to construct a discounted stochastic game (DSG) model of the emergence of equilibrium network dynamics that fully takes into account the feedback between network structure, strategic behavior, and risk. Based on our definition of systemic risk we also propose a formal definition of tipping points. Using these tools we provide a strategic approach to making global assessments of systemic risk in temporary financial networks. Our approach is based on three key facts: (1) the equilibrium dynamics which emerge from the game of network formation generate finitely many disjoint basins of attraction as well as finitely many ergodic measures (implying that, starting from any temporary financial network, in finite time with probability one, the dynamic sequence of networks arrives at one of these basins, and once there, stays there), (2) each basin of attraction is homogenous with respect to its default characteristics (meaning that if a basin contains networks having a particular set of defaulted players, then all networks contained in this basin have the same set of defaulted players), and (3) the unique profile of basins generated by the equilibrium dynamics carries with it a unique set of tipping points (special networks) - and these tipping points provide an early warning of network failure.
Systemic Risk Centre Discussion Papers DP 62