Closed-Loop Nash Competition for Liquidity

TL;DR

This paper analyzes a multi-player stochastic differential game involving trading agents whose interactions through price impact influence their strategies and outcomes, demonstrating the existence of a closed-loop Nash equilibrium under certain conditions.

Contribution

It proves the existence of a closed-loop Nash equilibrium in a multi-agent trading game with price impact and compares its outcomes to open-loop solutions, highlighting coordination effects.

Findings

Existence of closed-loop Nash equilibrium when price impact is small

Agents' trading rates and performance improve towards a central-planner solution

The effect of coordination on trading behavior is modest for realistic parameters

Abstract

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.