Discussion of Fairness and Implementability in Stackelberg Security Games

Abstract

In this article we discuss the impact of fairness constraints in Stackelberg Security Games. Fairness constraints can be used to avoid discrimination at the moment of implementing police patrolling. We present two ways of modelling fairness constraints, one with a detailed description of the population and the other with labels. We discuss the implementability of these constraints. In the case that the constraints are not implementable we present models to retrieve pure strategies in a way that they are the closest in average to the set of fairness constraints.

Playing Stackelberg Security Games in perfect formulations

“…After solving the compact formulation and obtaining the vector of marginal probabilities, we decompose it into feasible defender strategies. As was shown by Bucarey and Labbé [6], the defense marginal probability vector can be implemented universally.…”

“…Bucarey and Labbé [6] studied the problem of ensuring fairness in police patrolling to prevent discrimination when implementing surveillance. A set of targets J is protected, and the defender has m homogeneous security resources.…”

“…The defender's strategy is observed by the attackers, who respond optimally. Due to its importance in security applications, and being the dominant modeling choice in the literature [24,39,19,5,6,25], we find a Strong Stackelberg Equilibrium (SSE), i.e., in case of a tie between different possible responses of the follower, the most convenient response for the leader is chosen.…”