Hierarchical Competition as Equilibrium Program With Equilibrium Constraints Towards Security-Enhanced Wireless Networks

Abstract

Information security is a critical yet challenging issue for wireless communications. In this paper, we consider the distributed resource competition in a network that consists of both security-oriented users (SeUs) and regular users (ReUs) which, respectively, intend for secrecy rate and transmission rate maximization. To enhance wireless security, the SeUs are given higher priorities such that they are allowed to take action first in the competition, which gives rise to the multi-leader-follower hierarchical game formulation where the SeUs are the leaders in the upper layer and ReUs are the followers in the lower layer. However, the solution to the lower sub-game among the ReUs, in the form of a Nash equilibrium parameterized by the upper strategy, lacks closed-form expression, which hinders us from solving the hierarchical game effectively. To tackle this issue, we first consider the case with one leader and reformulate the game as a mathematical program with equilibrium constraints (MPEC). Then, the MPEC is transformed as a single-level optimization and solved through successive concave approximation. For the general case that comprises multiple leaders, the equilibrium program with equilibrium constraints (EPEC) is introduced for the game reformulation. Due to the inherent difficulties of EPEC, the relaxed concept of local Nash equilibrium (LNE) is introduced as the solution. Furthermore, the existence and uniqueness of the LNE are investigated with the variational inequality-based analysis. Finally, simulation results are provided to corroborate our theoretical findings.