Title: A two-player price impact game

 

Abstract:

We study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank, Soner, and Voss (2017), both facing common aggregated temporary and permanent price impact à la Almgren and Chriss. The resulting stochastic linear quadratic differential game with terminal state constraints allows for an explicitly available open loop Nash equilibrium in feedback form. our results reveal how the equilibrium strategies of the two players take into account the other agent's trading targets: either in an exploitatory intent or by providing liquidity to the competitor, depending on the ratio between temporary and permanent price impact. These insights complement existing studies in the literature on predatory trading games examined in the context of optimal portfolio liquidation problems.