# Stackelberg vs. Nash in Security Games: An Extended Investigation of Interchangeability, Equivalence, and Uniqueness

arXiv: https://arxiv.org/abs/1401.3888 · HTML: https://mlsanity.com/paper/1401.3888/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2014.

## Built on by (most cited first, 11 of 11)

- [Sample-Efficient Learning of Stackelberg Equilibria in General-Sum Games](https://mlsanity.com/paper/2102.11494/) (2021)
- [Learning in Stackelberg Games with Non-myopic Agents](https://mlsanity.com/paper/2208.09407/) (2022)
- [ApproxED: Approximate exploitability descent via learned best responses](https://mlsanity.com/paper/2301.08830/) (2023)
- [Rational Adversaries and the Maintenance of Fragility: A Game-Theoretic Theory of Rational Stagnation](https://mlsanity.com/paper/2510.22232/) (2025)
- [A Scalable Approach to Solving Simulation-Based Network Security Games](https://mlsanity.com/paper/2602.16564/) (2026)
- [Differentially Private Auditing Under Strategic Response](https://mlsanity.com/paper/2605.07674/) (2026)
- [Learning Generative Deception Strategies in Combinatorial Masking Games](https://mlsanity.com/paper/2109.11637/) (2021)
- [Learning to Defend by Attacking (and Vice-Versa): Transfer of Learning in Cybersecurity Games](https://mlsanity.com/paper/2306.02165/) (2023)
- [VISER: A Tractable Solution Concept for Games with Information Asymmetry](https://mlsanity.com/paper/2307.09652/) (2023)
- [Structured but Fragile: On the Limits of LLMs in Cybersecurity Decision-Making](https://mlsanity.com/paper/2608.20966/) (2026)
- [When Does Randomized Oversight Align AI Agents That Can Conceal?](https://mlsanity.com/paper/2609.38262/) (2026)

## Abstract (arXiv)

There has been significant recent interest in game-theoretic approaches to security, with much of the recent research focused on utilizing the leader-follower Stackelberg game model. Among the major applications are the ARMOR program deployed at LAX Airport and the IRIS program in use by the US Federal Air Marshals (FAMS). The foundational assumption for using Stackelberg games is that security forces (leaders), acting first, commit to a randomized strategy; while their adversaries (followers) choose their best response after surveillance of this randomized strategy. Yet, in many situations, a leader may face uncertainty about the follower's surveillance capability. Previous work fails to address how a leader should compute her strategy given such uncertainty. We provide five contributions in the context of a general class of security games. First, we show that the Nash equilibria in security games are interchangeable, thus alleviating the equilibrium selection problem. Second, under a natural restriction on security games, any Stackelberg strategy is also a Nash equilibrium strategy; and furthermore, the solution is unique in a class of security games of which ARMOR is a key exemplar. Third, when faced with a follower that can attack multiple targets, many of these properties no longer hold. Fourth, we show experimentally that in most (but not all) games where the restriction does not hold, the Stackelberg strategy is still a Nash equilibrium strategy, but this is no longer true when the attacker can attack multiple targets. Finally, as a possible direction for future research, we propose an extensive-form game model that makes the defender's uncertainty about the attacker's ability to observe explicit.