Coincidence analysis of Stackelberg and Nash equilibria in three-player leader-follower security games

TL;DR

This paper investigates the conditions under which Stackelberg and Nash equilibria coincide in three-player leader-follower security games, providing theoretical criteria and practical applications for strategic decision-making.

Contribution

It introduces necessary and sufficient conditions for equilibrium coincidence, offers criteria for verifying equilibrium strategies, and analyzes their closeness in practical security scenarios.

Findings

Identifies when SE and NE are equivalent in three-player security games.

Provides bounds on the deviation between SE and NE when they do not coincide.

Demonstrates the applicability of theoretical results in cybersecurity and secure transmission cases.

Abstract

There has been significant recent interest in leader-follower security games, where the leader dominates the decision process with the Stackelberg equilibrium (SE) strategy. However, such a leader-follower scheme may become invalid in practice due to subjective or objective factors, and then the Nash equilibrium (NE) strategy may be an alternative option. In this case, the leader may face a dilemma of choosing an SE strategy or an NE strategy. In this paper, we focus on a unified three-player leader-follower security game and study the coincidence between SE and NE. We first explore a necessary and sufficient condition for the case that each SE is an NE, which can be further presented concisely when the SE is unique. This condition not only provides access to seek a satisfactory SE strategy but also makes a criterion to verify an obtained SE strategy. Then we provide another appropriate condition for the case that at least one SE is an NE. Moreover, since the coincidence condition may not always be satisfied, we describe the closeness between SE and NE, and give an upper bound of their deviation. Finally, we show the applicability of the obtained theoretical results in several practical security cases, including the secure transmission problem and the cybersecurity defense.