Efficient broadcast communication in the presence of inside attackers: A non-cooperative game

Abstract

We study the problem of designing an efficient broadcast communication system in the presence of inside attackers from a Game Theory perspective. The network consists of a server that pre-assigns key sets to users some of whom may be malicious, either compromised or inherently selfish. The keys are mapped to communication channels unique in time and frequency, and the server broadcasts access information on those channels selectively. The goal of the server would be to deliver information to users using as fewer channels as possible. The malicious users, on the other hand, collude to selectively jam channels that their keys map to and keep as many users as possible from accessing the information while remaining undetected. This interaction of a server and inside attackers can be modeled as a 2-person game with server's payoff defined as the number of honest users who receive broadcast information as a function of the channels being used for broadcast, and the traitors' payoff defined as the number of honest users affected by jamming as a function of the channels being jammed. Our main contribution is the modeling of this server/intruder interaction as a non-cooperative game. Understanding that transmission as well as jamming cost depends on the key (channel) based on the number of users who own them and thus the amount of information it may reveal about a jammer, we assign a generic weight on the player's strategies yielding a generic payoff function. For simplicity, we first assume that both of the players are rational and that they have complete information about each other's payoff function and strategy space. With this, we derive a closed expression for the Nash Equilibrium (NE). Furthermore, we show that the complexity for computing the NE under our formulation is polynomial in the number of users. Then, we discuss preliminary steps required to arrive at the same game formulation without assuming complete information about player strategies, their payoffs and their rationality.