The rival might be not smart: Revising a CDMA jamming game
Andrey Garnaev, Wade K. Trappe · 2018
Due to the shared and open-access nature of the wireless medium, wireless networks are vulnerable to interference in the form of jamming attacks. In the research literature, game theory is a commonly employed tool to describe such jammming attacks as well as to design anti-jamming (defense) strategies. An advantage of such an approach is that it allows one to consider the adversary as a smart agent, who flexibly responds to the action of the other agents. In this paper, we put forward a question: what happen if the rival is smart? How does a priori knowledge about this impact on the rivals strategies. We formulate a jamming problem in a CDMA-style network as a Bayesian game between a jammer and a user with two-sided incomplete information about the type of rival it faces. We prove that the equilibrium exists and is unique. Closed form criteria to establish whether the equilibrium is an inner or boundary equilibrium is established. We derive monotonicity properties for the superposition of the two best response strategies, which allows us to develop an algorithm based on the bisection method to find the fixed point (i.e. equilibrium) of this superposition of best response strategies. Our algorithm can be considered as a learning algorithm since it allows to reduce the zone of uncertainty for the equilibrium by a half per iteration.