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Convex-Concave Zero-Sum Stochastic Stackelberg Games

Zero-sum stochastic Stackelberg games can be used to model a large class of problems, ranging from economics to human robot interaction. In this paper, we develop policy gradient methods to solve these games from noisy gradient estimates computed from observed trajectories of play. We prove that our algorithms converge to Stackelberg equilibrium in polynomial time when the games are convex-concave. We also prove that reach-avoid problems are naturally modeled as convex-concave zero-sum stochastic Stackelberg games. Finally, we run experiments which demonstrate that modeling reach-avoid problems as Stackelberg games leads to solutions which are safer, thus less likely to result in collisions, and liver, thus more likely to reach their goals, than alternative solutions, in particular Nash equilibrium.

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