Power Allocation in Team Jamming Games in Wireless Ad Hoc Networks

TL;DR

This paper models power allocation in team-based jamming games within wireless ad hoc networks as a zero-sum differential game, deriving conditions for optimal strategies and Nash equilibria through Isaacs' approach.

Contribution

It introduces a novel differential game framework for power allocation in team jamming scenarios, providing conditions for Nash equilibrium existence.

Findings

Existence of pure strategy Nash equilibrium under certain physical parameters.

Necessary conditions for optimal power trajectories derived from Isaacs' approach.

Simulation results demonstrate the effectiveness of the proposed game-theoretic strategies.

Abstract

In this work, we study the problem of power allocation in teams. Each team consists of two agents who try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function 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 {\it{Isaacs'}} approach to obtain the necessary conditions for the optimal trajectories. This leads to a continuous-kernel power allocation game among the players. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy Nash equilibrium (PSNE). Finally, we present simulation results for the case when the agents are holonomic.