  We consider a novel class of portfolio liquidation games with market drop-out
("absorption"). More precisely, we consider mean-field and finite player
liquidation games where a player drops out of the market when her position hits
zero. In particular round-trips are not admissible. This can be viewed as a no
statistical arbitrage condition. In a model with only sellers we prove that the
absorption condition is equivalent to a short selling constraint. We prove that
equilibria (both in the mean-field and the finite player game) are given as
solutions to a non-linear higher-order integral equation with endogenous
terminal condition. We prove the existence of a unique solution to the integral
equation from which we obtain the existence of a unique equilibrium in the MFG
and the existence of a unique equilibrium in the $N$-player game. We establish
the convergence of the equilibria in the finite player games to the obtained
mean-field equilibrium and illustrate the impact of the drop-out constraint on
equilibrium trading rates.
