  We study a multi-player 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.
