Stackelberg games of large population multi-agent systems: Centralized and distributed strategies

In the paper, Stackelberg games are investigated for large population multi-agent systems involving a major agent and a large number of minor agents. In each stage of the game, the major agent first makes decisions, and then all minor agents give strategies simultaneously. A set of centralized Stackelberg equilibrium strategy is first provided, and then, by the mean field approach and the brute force method, a set of distributed strategies is given. Under a mild condition, it is shown that the closed-loop system is uniformly stable and the set of distributed strategies is an ε-Stackelberg equilibrium.