We consider the problem of power control for two independent relay-assisted wireless systems that operate in the same spectral band. A general scenario where both systems are allowed to select between amplify-and-forward relaying and decode-and-forward relaying is studied. We adopt a game-theoretic approach and show that once both systems act non-cooperatively to optimize their own rate, they can always reach a unique Nash equilibrium (NE) from an arbitrary starting point in a totally distributed and asynchronous manner. We also provide insights on the impacts of network topology and relaying protocols on the sum rate performance of the NE through extensive numerical results.
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