A Non-Zero Sum Bandwidth Scanning Game with a Sophisticated Adversary

Detecting malicious users (adversaries) or unlicensed activities is a crucial problem facing dynamic spectrum access. Traditionally, in such a problem, the adversary is considered to be one who wants to get achieve malicious goal undetected. In this paper we deal with a new type of adversary, called sophisticated adversary, who, besides the basic goal of being malicious and undetected, it also wants to achieve this in the most unpredictable way. As a metric for such unpredictability we consider the entropy of adversary strategy. We model this problem by a nonzero-sum two players resource allocation game. One of the players, called the Scanner, wants to detect the sophisticated adversary. The other player (adversary), called the Invader, wants to find a trade-off between two goals: to sneak bandwidth usage undetected and to achieve such sneaking in the most unpredictable way. The equilibrium is found in closed form, and its dependence on communication network parameters is illustrated. Finally, weighting coefficients for the basic and secondary goals of the Invader are optimized via Nash bargaining.