Security Games and Combinatorial Optimization 1 Zero-sum Security Games -a Unified View

• Set of defender pure strategies, denoted as E . We will use e(∈ E) to denote a generic pure strategy. Crucially, any e can be viewed as a subset of [n], denoting the protected (a.k.a., covered) targets by this pure strategy. In particular, the defender has multiple security resources; One pure strategy is a feasible allocation of these resources – e is precisely the set of covered targets in this feasible resource allocation. Equivalently, one can view e ∈ {0, 1} as a binary vector where the value-1 entries specify the covered targets. For convenience, we will use this representation throughout this note. A defender mixed strategy is a distribution p ∈ ∆|E| over elements in E . Here ∆m = {p ∈ R : ∑m i=1 pi = 1; pi ≥ 0} is the m-dimensional simplex, consisting of all the (discrete) distributions over support of size m.