# Safe Search for Stackelberg Equilibria in Extensive-Form Games

arXiv: https://arxiv.org/abs/2102.01775 · HTML: https://mlsanity.com/paper/2102.01775/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 26 references that are in the map.
- First posted on arXiv 2 Feb 2021.

## Builds on (most cited first, 4 of 4)

- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [Safe and Nested Subgame Solving for Imperfect-Information Games](https://mlsanity.com/paper/1705.02955/) (2017)
- [Solving Imperfect Information Games Using Decomposition](https://mlsanity.com/paper/1303.4441/) (2013)
- [Solving Large Sequential Games with the Excessive Gap Technique](https://mlsanity.com/paper/1810.03063/) (2018)

## Built on by (most cited first, 3 of 3)

- [Search in Imperfect Information Games](https://mlsanity.com/paper/2111.05884/) (2021)
- [Multi-defender Security Games with Schedules](https://mlsanity.com/paper/2311.16392/) (2023)
- [Safe Subgame Resolving for Extensive Form Correlated Equilibrium](https://mlsanity.com/paper/2212.14317/) (2022)

## Abstract (arXiv)

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.