This work addresses the challenge “how do we make better security decisions?” and it develops techniques to support human decision making and algorithms which enable well-founded cyber security decisions to be made. In this paper we propose a game theoretic model which optimally allocates cyber security resources such as administrators’ time across different tasks. We first model the interactions between an omnipresent attacker and a team of system administrators seen as the defender, and we have derived the mixed Nash Equilibria (NE) in such games. We have formulated general-sum games that represent our cyber security environment, and we have proven that the defender’s Nash strategy is also minimax. This result guarantees that independently from the attacker’s strategy the defender’s solution is optimal. We also propose Singular Value Decomposition (SVD) as an efficient technique to compute approximate equilibria in our games. By implementing and evaluating a minimax solver with SVD, we have thoroughly investigated the improvement that Nash defense introduces compared to other strategies chosen by common sense decision algorithms. Our key finding is that a particular NE, which we call weighted NE, provides the most effective defense strategy. In order to validate this model we have used real-life statistics from Hackmageddon, the Verizon 2013 Data Breach Investigation report, and the Ponemon report of 2011. We finally compare the game theoretic defense method with a method which implements a stochastic optimization algorithm.