  We consider $n$ risk-averse agents who compete for liquidity in an
Almgren--Chriss market impact model. Mathematically, this situation can be
described by a Nash equilibrium for a certain linear-quadratic differential
game with state constraints. The state constraints enter the problem as
terminal boundary conditions for finite and infinite time horizons. We prove
existence and uniqueness of Nash equilibria and give closed-form solutions in
some special cases. We also analyze qualitative properties of the equilibrium
strategies and provide corresponding financial interpretations.
