  Repeated game has long been the touchstone model for agents' long-run
relationships. Previous results suggest that it is particularly difficult for a
repeated game player to exert an autocratic control on the payoffs since they
are jointly determined by all participants. This work discovers that the scale
of a player's capability to unilaterally influence the payoffs may have been
much underestimated. Under the conventional iterated prisoner's dilemma, we
develop a general framework for controlling the feasible region where the
players' payoff pairs lie. A control strategy player is able to confine the
payoff pairs in her objective region, as long as this region has feasible
linear boundaries. With this framework, many well-known existing strategies can
be categorized and various new strategies with nice properties can be further
identified. We show that the control strategies perform well either in a
tournament or against a human-like opponent.
