Multi-layer hierarchical approach to double sided jamming games among teams of mobile agents

In this paper, we study the trade off in resource allocation between malicious intrusion (jamming) and communication/ coordination by two teams of mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they distribute their available power between the tasks of communication and jamming the communication network nodes of the other team. This is a generalization of our earlier work in [7] which considered the special case when each team consists of only two agents. Here we consider the nontrivial extension to multiple agents (in each 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 (where the teams are the actual players in the zero-sum game) and use Isaacs´ approach to obtain necessary conditions for the corresponding trajectories. The solution to the optimal control problem for each team in turn depends on the solution to the power allocation problem for each agent. The power allocation problem is a non-zero sum game between the two teams, and we present sufficient conditions for the existence of a pure strategy Nash equilibrium. Finally, we provide some simulation results to validate the approach taken.