  In general-sum stochastic games, a stationary Stackelberg equilibrium (SSE)
does not always exist, in which the leader maximizes leader's return for all
the initial states when the follower takes the best response against the
leader's policy. Existing methods of determining the SSEs require strong
assumptions to guarantee the convergence and the coincidence of the limit with
the SSE. Moreover, our analysis suggests that the performance at the fixed
points of these methods is not reasonable when they are not SSEs. Herein, we
introduced the concept of Pareto-optimality as a reasonable alternative to
SSEs. We derive the policy improvement theorem for stochastic games with the
best-response follower and propose an iterative algorithm to determine the
Pareto-optimal policies based on it. Monotone improvement and convergence of
the proposed approach are proved, and its convergence to SSEs is proved in a
special case.
