Interference Pricing for SINR-Based Random Access Game

In this paper, we study the problem of random access with interference pricing in wireless ad hoc networks using non-cooperative game theory. While most of the previous works in random access games are based on the protocol model, we analyze the game under the more accurate signal-to-interference-plus-noise-ratio (SINR) model. First, under the setting with fixed interference linear pricing, we characterize the existence of the Nash equilibrium (NE) in the random access game. In particular, when the utility functions of all the players satisfy a risk aversion condition, we show that the game is a S-modular game and characterize the convergence of the strategy profile to the NE. Then, under the setting with adaptive interference linear pricing, we propose an iterative algorithm that aims to solve the network utility maximization (NUM) problem. Convergence of the solution to a Karush-Kuhn-Tucker (KKT) point of the NUM problem is studied. It can be shown that the solution obtained under the protocol model may result in starvation for some users due to the inaccurate interference pricing. Simulation results show that our proposed algorithm based on the SINR model achieves a higher average utility than the algorithm based on the protocol model and a carrier sense multiple access (CSMA) scheme implemented in a slotted time system.