The Stackelberg game model, where a leader commits to a strategy and the
follower best responds, has found widespread application, particularly to
security problems. In the security setting, the goal is for the leader to
compute an optimal strategy to commit to, in order to protect some asset. In
many of these applications, the parameters of the follower utility model are
not known with certainty. Distributionally-robust optimization addresses this
issue by allowing a distribution over possible model parameters, where this
distribution comes from a set of possible distributions. The goal is to
maximize the expected utility with respect to the worst-case distribution. We
initiate the study of distributionally-robust models for computing the optimal
strategy to commit to. We consider the case of normal-form games with
uncertainty about the follower utility model. Our main theoretical result is to
show that a distributionally-robust Stackelberg equilibrium always exists
across a wide array of uncertainty models. For the case of a finite set of
possible follower utility functions we present two algorithms to compute a
distributionally-robust strong Stackelberg equilibrium (DRSSE) using
mathematical programs. Next, in the general case where there is an infinite
number of possible follower utility functions and the uncertainty is
represented by a Wasserstein ball around a finitely-supported nominal
distribution, we give an incremental mixed-integer-programming-based algorithm
for computing the optimal distributionally-robust strategy. Experiments
substantiate the tractability of our algorithm on a classical Stackelberg game,
showing that our approach scales to medium-sized games.

本文研究了基于分布鲁棒优化的 Stackelberg 游戏模型，特别是在不确定下属效用模型的情况下，寻找最优策略以保护某些资产。我们的研究表明，在广泛的不确定模型下，分布鲁棒 Stackelberg 均衡始终存在。当存在无限个下属效用函数且不确定性由支持有限名义分布周围的 Wasserstein 球表示时，我们提出了一种基于混合整数规划的增量算法来计算最优的分布鲁棒策略。实验结果显示，我们的方法可扩展到中等规模的 Stackelberg 游戏，从而验证了算法的可行性。