Closed‐loop Nash competition for liquidity

Abstract

AbstractWe study a multiplayer stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed‐loop Nash equilibrium exists if the price impact parameter is small enough. Compared to the corresponding open‐loop Nash equilibrium, both the agents' optimal trading rates and their performance move towards the central‐planner solution, in that excessive trading due to lack of coordination is reduced. However, the size of this effect is modest for plausible parameter values.