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This paper considers a multiuser single-relay wireless network, where the relay gets paid for helping users forward signals, and the users pay to receive the relay service. We study the relay power allocation and pricing problems and model the interaction between the users and the relay as a two-level Stackelberg game. In this game, the relay, which is modeled as the service provider and the leader of the game, sets the relay price to maximize its revenue, whereas the users are modeled as customers and followers who buy power from the relay for higher transmission rates. We use a bargaining game to model the negotiation among users to achieve a fair allocation of relay power. Based on the proposed fair relay power allocation rule, the optimal relay power price that maximizes the relay revenue is derived analytically. Simulation shows that the proposed power allocation scheme achieves higher network sum rate and relay revenue than the even power allocation. Furthermore, compared with the sum-rate-optimal solution, simulation shows that the proposed scheme achieves better fairness with comparable network sum rate for a wide range of network scenarios. The proposed pricing and power allocation solutions are also shown to be consistent with the laws of supply and demand.

Power Allocation and Pricing in Multiuser Relay Networks Using Stackelberg and Bargaining Games