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In this paper, we consider a wireless amplify-and-forward relay network with one relay node and multiple source-destination pairs/users and propose a pricing framework that enables the relay to set prices to maximize either its revenue or any desirable system utility. Specifically, depending on the quality of the received signals, the relay sets prices and correspondingly charges the users utilizing its resources for their transmissions. The price is determined in such a way that the relay's revenue or system utility is maximized. Given the specified price, the users competitively employ the relay node to forward their signals. We model each user as a rational player, which aims at maximizing its own net utility through power allocation, and analyze the competition among the users within the framework of noncooperative game theory. It is shown that, in the game played by the users, there always exists a unique pure Nash equilibrium point that can be achieved through distributed iterations. Next, subject to the availability of complete information about the users at the relay, we propose a low-complexity uniform pricing algorithm and an optimal differentiated pricing algorithm, in which the relay either charges the users at a suboptimal uniform price or charges different users at different prices. We also show that, by applying the differentiated pricing algorithm that enforces the users to transmit at certain power levels, any system utility can be maximized. Extensive simulations are conducted to quantify the performance of the proposed methods.