  It was shown in Flesch and Solan (2022) with a rather involved proof that all
two-player stochastic games with finite state and action spaces and
shift-invariant payoffs admit an $\epsilon$-equilibrium, for every
$\epsilon>0$. Their proof also holds for two-player absorbing games with
tail-measurable payoffs. In this paper we provide a simpler proof for the
existence of $\epsilon$-equilibrium in two-player absorbing games with
tail-measurable payoffs, by combining recent mathematical tools for such payoff
functions with classical tools for absorbing games.
