Closed-Loop Nash Competition for Liquidity

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. Mathematics Subject Classification (2010): 49N90, 91A25, 91G10, 93E20 JEL Classification: C73, C02, C61, G11, G12

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