Closed‐loop Nash competition for liquidity

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