We adopt a game theoretic approach for the analysis of wireless channels where the users are modeled as rational and selfish players interested in maximizing the utilities they obtain from the network. In the fading multiple access channel, we first show that the sum-rate optimal point on the boundary of the capacity region is the unique Nash Equilibrium of the corresponding water-filling game. By introducing the base-station as a player interested in maximizing a weighted sum of the individual rates, we then propose a Stackelberg formulation in which the base-station is the designated game leader. We show that this formulation allows for achieving all the corner points of the capacity region, in addition to the sum-rate optimal point. Then we consider the cooperative multiple access channel, where we show that non-cooperation is the only Nash Equilibrium. By introducing a relay node designated as the leader of a Stackelberg game, we show that cooperation emerges at the equilibrium point under some typical operating scenarios. Finally, we establish similar results for the interference channel.

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