  In this paper, we consider a new network security game wherein an attacker
and a defender are battling over "multiple" targets. This type of game is
appropriate to model many current network security conflicts such as Internet
phishing, mobile malware or network intrusions. In such attacks, the attacker
and the defender need to decide how to allocate resources on each target so as
to maximize his utility within his resource limit. We model such a
multi-dimensional network security game as a constrained non-zero sum game. Two
security breaching models, the product-form and the proportion-form, are
considered. For each breaching model, we prove the existence of a unique Nash
equilibrium (NE) based on Rosen's theorem and propose efficient algorithms to
find the NE when the games are strictly concave. Furthermore, we show the
existence of multiple NEs in the product-form breaching model when the strict
concavity does not hold. Our study sheds light on the strategic behaviors of
the attacker and the defender, in particular, on how they allocate resources to
the targets which have different weights, and how their utilities as well as
strategies are influenced by the resource constraints.
