A Prospect Theoretical Extension of a Communication Game Under Jamming

Abstract

In this paper, we consider how subjectivity affects the problem of reliable communication. To model subjective factor we formulate a prospect theoretical (PT) extension of a zero sum game involving a primary user (PU) that must communicate with one of n users, while avoiding being jammed by an adversary. We prove that the PT equilibrium strategies, which are generalizations of the Nash equilibrium, exist for any probability weighting functions that models the corresponding subjective factors. Moreover, the PT-equilibrium strategy for the adversary is unique, and it can be found in water-filling form. We establish conditions for the PT-equilibrium of the PU to be unique. If PT-equilibrium of the PU is not unique, then a continuum of PT-equilibria arise. All of the PT-equilibria are found in water-filling form, and a hierarchical relationship between the derived water-filling equations is established. Finally, the sensitivity of the PT equilibrium strategies to environmental parameters is theoretically proven and numerically illustrated.