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

Multi-dimensional Network Security Game: How do attacker and defender battle on parallel targets?