Safe Search for Stackelberg Equilibria in Extensive-Form Games

TL;DR

This paper introduces a novel online search method for computing Stackelberg equilibria in extensive-form games, improving solution quality over offline methods and enabling larger game analysis with theoretical guarantees.

Contribution

It presents a theoretically sound online search approach that refines pre-computed solutions for Stackelberg equilibria, enhancing scalability and practical applicability.

Findings

Guarantees no worse than the offline blueprint strategy

Enables solving larger games than offline methods

Cast as a smaller Stackelberg problem for efficiency

Abstract

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.