Mean-Field-Type Stackelberg Games

This chapter focuses on the two-level hierarchical mean-field-type game problem known as Stackelberg games. This class of games can be easily extended to the multiple level case. Stackelberg games consist of only two players, which are known as a leader and a follower. The leader who moves first, decides an optimal strategy after anticipating the best response of the follower. Then, the follower eventually chooses the anticipated best response to optimize its cost or payoff. When there are two or more decision-makers in this sequential strategic scheme, the Stackelberg game is called hierarchical game and it becomes more interesting due to its multi-layer structure including various forms of information. The players act in sequential order such that each one of them is a leader for the previous and a follower of the next player in the hierarchy. This topic is quite relevant and getting special importance because there is a large variety of engineering applications whose configuration is built in a hierarchical manner. Over the end of this chapter we present a numerical example for two decision-makers, and incorporating Brownian motion and Poisson jumps.