Safe Search for Stackelberg Equilibria in Extensive-Form Games
This work provides an incremental improvement for researchers and practitioners working on security applications that can be modeled as Stackelberg games, enabling them to handle larger problem instances.
This paper tackles the problem of computing Stackelberg equilibria in extensive-form games, which are relevant for security applications. The authors propose a search-based method that computes an approximate "blueprint" solution offline and then improves it online for specific subgames. This approach allows for approximately solving significantly larger games compared to purely offline methods.
Stackelberg equilibrium is a solution concept in two-player games where the leader has commitment rights over the follower. In recent years, it has become a cornerstone of many security applications, including airport patrolling and wildlife poaching prevention. Even though many of these settings are sequential in nature, existing techniques pre-compute the entire solution ahead of time. In this paper, we present a theoretically sound and empirically effective way to apply search, which leverages extra online computation to improve a solution, to the computation of Stackelberg equilibria in general-sum games. Instead of the leader attempting to solve the full game upfront, an approximate "blueprint" solution is first computed offline and is then improved online for the particular subgames encountered in actual play. We prove that our search technique is guaranteed to perform no worse than the pre-computed blueprint strategy, and empirically demonstrate that it enables approximately solving significantly larger games compared to purely offline methods. We also show that our search operation may be cast as a smaller Stackelberg problem, making our method complementary to existing algorithms based on strategy generation.