Playing with fire? A mean‐field game analysis of fire sales and systemic risk under regulatory capital constraints

Abstract We analyze the effect of regulatory capital constraints on financial stability in a large homogeneous banking system using a mean‐field game (MFG) model. Each bank holds cash and a tradable risky asset. Banks choose absolutely continuous trading rates in order to maximize expected terminal equity, with trades subject to transaction costs. Capital regulation requires equity to exceed a fixed multiple of the position in the tradable asset; breaches trigger forced liquidation. The asset drift depends on changes in average asset holdings across banks, so aggregate de‐leveraging creates contagion effects, leading to an MFG. We discuss the coupled forward‐backward partial differential equation (PDE) system characterizing equilibria of the MFG and solve the constrained MFG numerically. Experiments demonstrate that capital constraints accelerate de‐leveraging and limit risk‐bearing capacity. In some regimes, simultaneous breaches trigger liquidation cascades. Finally, we discuss several policy mechanisms for enhancing financial stability.