Application of the replicator equation to decision-making processes in border security

The replicator equations are first-order (in time), nonlinear differential equations which can be used to model the time evolution of probabilities in evolutionary game theory. They are obtained by assuming that the percentage rate of change of a probability be simply proportional to the difference between a payoff and some average payoff. Here we apply these equations to obtain the time evolution two players' strategies in a zero-sum game which models the illegal transport of a commodity across a national border and of the efforts of agents to intercept it.