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Power control for uplink channels with non- cooperative and rational mobile stations (MS) can be studied in the framework of game theory. In this paper, we investigate the optimal design of a multi-antenna access point (AP) in such a scenario by modelling the interaction between the AP on one side, and the distributed set of MSs on the other, as a Stackelberg game. As a game leader, the AP determines the network parameters (bandwidth and the number of receiving antennas) for the power control game played between the MSs (follower), so as to maximize the network utility per system resource (bandwidth and antennas). Two game models are considered, whereby the network utility is measured either in terms of power minimization or power efficiency maximization. Extensive numerical results provide insights into the properties of the optimal design.