1. A method of determining a leader's strategy for a security domain, the method comprising: formulating, using a processor, a leader's policy; formulating, using the processor, a linear optimization problem with integer variables, including a linear objective, that the follower solves to find its optimal response to the leader's policy; maximizing the payoff of the leader, given that the follower uses an optimal response that is function of the leader's policy, and wherein the leader uses a policy that is a mixed strategy, a k-uniform policy, or a pure strategy; formulating the problem of maximizing the payoff of the leader as a mixed-integer linear program (MILP); performing a decomposition of the MILP, wherein a decomposed MILP is produced; solving the decomposed MILP, wherein a solved MILP is produced; and directing a patrolling strategy of an agent within the security domain based on the solved MILP.