Stackelberg solution of dynamic game with constraints

The paper presents the solution of the dynamic closed-loop Stackelberg game, discusses the interpretation of the leader's strategy as the formalization of the intuitive notion of threat or incentive, and considers the limitations of the Stackelberg solution concept which within the dynamic context is applicable only to the situations where the realization of the leader's strategy in the course of the game is ensured by a binding contract. It is shown that the supremum S of the leader's payoff over his strategy space can be computed by solving a maximin problem and an optimization problem. In general the leader can achieve the payoff arbitrarily close to S by means of ε - Stackelberg strategies, but the Stackelberg strategy ensuring the payoff equal to S exists only in rather exceptional cases /e.g. the linear-quadratic game/.