On the steady state solution of a two-by-two dynamic jamming game with cumulative power constraints

It is noted that the process of jamming can be modeled as a two-person zero-sum noncooperative dynamic game played between a communicator and a jammer over a number of discrete time instants. The simplest case is when, at each instant, the communicator and jammer randomize their strategies between idleness and transmission. The payoff (throughput) matrix is then two-by-two, with one variable parameter. The payoff function is the average throughput summed over time, to be optimized subject to cumulative power constraints. The authors find an analytical steady-state solution for this game played over an infinite time duration. Results show that when the throughput parameter is lower than a threshold, the optimal strategies are mixed, and the payoff increment constant; otherwise the strategies are pure, with the payoff increment exhibiting oscillatory behavior