Switching behavior in optimal communication strategies for team jamming games under resource constraints

In this paper, we address the issue of malicious intrusion in the communication network present in a team of autonomous vehicles. In our current scenario, we consider the special case of two teams with each team consisting of two mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they try to split their available power between the tasks of communication and jamming the nodes of the other team. Contrary to our earlier work, this paper addresses the scenario in which each player has an omni-directional antenna for jamming the communication between the members of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function adopted is the difference between the rates of erroneously transmitted bits of each team. We model the problem as a zero-sum differential game between the two teams and use Isaacs' approach to obtain the necessary conditions for the optimal trajectories. We model the adaptive modulation problem as a zero-sum matrix game which in turn gives rise to a continuous kernel game to handle power control. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy saddle-point equilibrium (PSSPE). This leads to a switching behavior in the optimal communication strategy within a team, over the time horizon of the entire game. This behavior is illustrated in our simulations for the case when the agents are holonomic.