Power Control in Relay-Assisted Anti-Jamming Systems: A Bayesian Three-Layer Stackelberg Game Approach

This paper investigates the multi-user power control problem in relay-assisted anti-jamming systems. Because of the hierarchical confrontation characteristics between users and jammer, we take the incomplete information and observation error into consideration and formulate an anti-jamming Bayesian three-layer Stackelberg game, in which primary users act as leaders, relay users act as vice-leaders, and jammer acts as a follower. Both users and jammer have the ability to sense others' transmission power and choose optimal power to realize the maximum of utility. Based on the backward induction method, we propose a multi-user hierarchical iterative algorithm to obtain the Stackelberg equilibrium (SE) and prove the existence and uniqueness of SE. Finally, simulation results are compared with the Nash equilibrium to verify the effectiveness of the proposed game. Moreover, both the influence of incomplete information and the observation error on utility are analyzed.