We deal with Stackelberg games in which a leader has access not only to the state information but also to information on the follower's strategy. We derive sufficient conditions for incentive schemes using information on the follower's strategies in both linear and non-linear differential games, and show that the incentive schemes using information on the follower's strategies depend on an initial state value. We also derive a sufficient condition for the incentive scheme using the follower's strategy in the linear quadratic differential game with infinite time interval.