A complete solution for two-person, single-stage, deterministic, stackelberg game

A method is presented to solve two-person, single-stage, deterministic, Stackelberg games. The approach lies on the delineation of the inducible region. If the leader is extremely powerful, he can induce the follower to do whatever he desires. However, the leader in general can only induce the follower\´s behavior to "certain extent" due to limited information, control, etc. In other words, there exists a region inside which the leader can induce the follower\´s behavior. Thus, the best the leader can do is to minimize his cost inside this region. In this paper, we delineate precisely the inducible region, and obtain a leader\´s optimal strategy, if it exists. In case that a Stackelberg strategy does not exist, we show that an ??-Stackelberg strategy always exists.