  In a single-state repeated game, zero-determinant strategies can unilaterally
force functions of the payoffs to take values in particular closed intervals.
When the explicit use of a determinant is absent from the analysis, they are
instead called autocratic. We extend their study to the setting of finite state
games with deterministic transitions. For a given game we find that the
endpoints of the intervals of enforceable values must satisfy fixed point
equations. From these extreme enforceable values we show it is always possible
to construct finite memory strategies to enforce a particular value. An
algorithm is presented which will approximate the enforceable values in each
state. Finally, we present formulas from which the exact solutions can be
recovered from the approximate solution.
