Dynamic Stackelberg games under open-loop complete information

Stackelberg games, which play extremely important roles in such fields as economics, management, politics and behavioral sciences, can be modelled as a bilevel optimization problem. There exist extensive literatures about static bilevel optimization problems. However, the studies on dynamic bilevel optimization problems are rather scarce in spite of the importance in explaining and predicting some phenomena rationally. In this paper, discrete time dynamic Stackelberg games with open loop complete state are revisited. An example, which comes from law field, is presented as an open-loop Stackelberg game to illuminate the rangy application of game theory. A property based on Bellman's equation is proposed without any restriction about inner point solution for open-loop Stackelberg games in this work. Moreover, we point out that open-loop Stackelberg games perform no better than both feedback and closed-loop dynamic Stackelberg games with complete information, which seems quite valuable to explain some social and economic phenomena.