A Generalization of Two-Player Stackelberg Games to Three Players

Two-player Stackelberg games and their applications to security are currently a very hot topic in the field of Algorithmic Game Theory [7]. In two-player Stackelberg games, instead of having the players move simultaneously, one player is designated as the leader and one as the follower. The game then works as follows: the leader chooses a strategy (possibly mixed) to commit to which the follower observes before choosing his response. A large part of the appeal of two-player Stackelberg games is the fact that they can be solved using linear programming in polynomial time in the size of the game [3]. One obvious question then, is whether or not this tractability can be extended to Stackelberg games with more players. This is addressed somewhat in [2], however the model presented relies on the followers obeying a signal from the leader, which is a very strong assumption. In this paper, I propose an alternative model with weaker assumptions and then analyze its complexity.