Solving Stackelberg games with uncertain observability

Abstract

Recent applications of game theory in security domains use algorithms to solve a Stackelberg model, in which one player (the leader) first commits to a mixed strategy and then the other player (the follower) observes that strategy and bestresponds to it. However, in real-world applications, it is hard to determine whether the follower is actually able to observe the leader’s mixed strategy before acting. In this paper, we model the uncertainty about whether the follower is able to observe the leader’s strategy as part of the game (as proposed in the extended version of Yin et al. [17]). We describe an iterative algorithm for solving these games. This algorithm alternates between calling a Nash equilibrium solver and a Stackelberg solver as subroutines. We prove that the algorithm finds a solution in a finite number of steps and show empirically that it runs fast on games of reasonable size. We also discuss other properties of this methodology based on the experiments.

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