# Multi-defender Security Games with Schedules

arXiv: https://arxiv.org/abs/2311.16392 · HTML: https://mlsanity.com/paper/2311.16392/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 30 references that are in the map.
- First posted on arXiv 28 Nov 2023.

## Builds on (most cited first, 3 of 3)

- [A Game-Theoretic Taxonomy and Survey of Defensive Deception for Cybersecurity and Privacy](https://mlsanity.com/paper/1712.05441/) (2017)
- [Deep Reinforcement Learning for Green Security Games with Real-Time Information](https://mlsanity.com/paper/1811.02483/) (2018)
- [Safe Search for Stackelberg Equilibria in Extensive-Form Games](https://mlsanity.com/paper/2102.01775/) (2021)

## Built on by (most cited first, 1 of 1)

- [Patrol Security Game: Defending Against Adversary with Freedom in Attack Timing, Location, and Duration](https://mlsanity.com/paper/2410.15600/) (2024)

## Abstract (arXiv)

Stackelberg Security Games are often used to model strategic interactions in high-stakes security settings. The majority of existing models focus on single-defender settings where a single entity assumes command of all security assets. However, many realistic scenarios feature multiple heterogeneous defenders with their own interests and priorities embedded in a more complex system. Furthermore, defenders rarely choose targets to protect. Instead, they have a multitude of defensive resources or schedules at its disposal, each with different protective capabilities. In this paper, we study security games featuring multiple defenders and schedules simultaneously. We show that unlike prior work on multi-defender security games, the introduction of schedules can cause non-existence of equilibrium even under rather restricted environments. We prove that under the mild restriction that any subset of a schedule is also a schedule, non-existence of equilibrium is not only avoided, but can be computed in polynomial time in games with two defenders. Under additional assumptions, our algorithm can be extended to games with more than two defenders and its computation scaled up in special classes of games with compactly represented schedules such as those used in patrolling applications. Experimental results suggest that our methods scale gracefully with game size, making our algorithms amongst the few that can tackle multiple heterogeneous defenders.