Analysis of an on-off jamming situation as a dynamic game

The process of communication jamming can be modeled as a two-person zero-sum noncooperative dynamic game played between a communicator (a transmitter-receiver pair) and a jammer. We consider a one-way time-slotted packet radio communication link in the presence of a jammer, where the data rate is fixed and (1) in each slot, the communicator and jammer choose their respective power levels in a random fashion from a zero and a positive value; (2) both players are subject to temporal energy constraints which account for protection of the communicating and jamming transmitters from overheating. The payoff function is the time average of the mean payoff per slot. The game is solved for certain ranges of the players' transmitter parameters. Structures of steady-state solutions to the game are also investigated. The general behavior of the players' strategies and payoff increment is found to depend on a parameter related to the payoff matrix, which me call the payoff parameter, and the transmitters' parameters. When the payoff parameter is lower than a threshold, the optimal steady-state strategies are mixed and the payoff increment constant over time, whereas when it is greater than the threshold, the strategies are pure, and the payoff increment exhibits oscillatory behavior