Multilevel Reverse Stackelberg Differential Games: Existence and Solution Approach for Affine Strategies

This article considers multilevel sequential differential games over fixed time interval. In this continuous time game structure, the leader controls the outcome by announcing a reverse Stackelberg strategy as a mapping from the decision spaces of the followers to his/her decision space. The leader constructs such a strategy based on the control of the followers, which can be determined up to the current time only, also called causal strategy. Existence of affine reverse Stackelberg strategy for multilevel differential games is proved, and a method to obtain such set of strategies is also presented. The structure of this game can be adopted to many application areas, in particular in decentralized continuous decision making situations such as marketing system, taxation and budget allocation. As compared to the existing literature, the result applies to more general game settings and hierarchical levels of decisions.