  This paper presents a new solution concept for multiplayer stochastic games,
namely, acceptable strategy profiles. For each player $i$ and state $s$ in a
stochastic game, let $w_i(s)$ be a real number. A strategy profile is
\emph{$w$-acceptable}, where $w=(w_i(s))$, if the discounted payoff to each
player $i$ at every initial state $s$ is at least $w_i(s)$, provided the
discount factor of the players is sufficiently close to 1. Our goal is to
provide simple strategy profiles that are $w$-acceptable for payoff vectors $w$
in which all coordinates are high.
