Robust Solutions for Multi-Defender Stackelberg Security Games

TL;DR

This paper introduces a robust model for Multi-defender Stackelberg Security Games that produces solutions resistant to small uncertainties, significantly improving defenders' utilities compared to traditional approaches.

Contribution

The paper formalizes a robust MSSG model, proves the existence of robust equilibria and cores, and provides efficient methods for constructing these solutions.

Findings

Robust solutions can substantially increase defenders' utilities.

Existence of robust approximate equilibrium in non-cooperative MSSGs.

Existence of robust approximate alpha-core in cooperative MSSGs.

Abstract

Multi-defender Stackelberg Security Games (MSSG) have recently gained increasing attention in the literature. However, the solutions offered to date are highly sensitive, wherein even small perturbations in the attacker's utility or slight uncertainties thereof can dramatically change the defenders' resulting payoffs and alter the equilibrium. In this paper, we introduce a robust model for MSSGs, which admits solutions that are resistant to small perturbations or uncertainties in the game's parameters. First, we formally define the notion of robustness, as well as the robust MSSG model. Then, for the non-cooperative setting, we prove the existence of a robust approximate equilibrium in any such game, and provide an efficient construction thereof. For the cooperative setting, we show that any such game admits a robust approximate alpha-core, provide an efficient construction thereof, and prove that stronger types of the core may be empty. Interestingly, the robust solutions can substantially increase the defenders' utilities over those of the non-robust ones.