Abstract
A Bayesian game-theoretic model is developed to design and analyze the resource allocation problem in -user fading multiple access channels (MACs), where the users are assumed to selfishly maximize their average achievable rates with incomplete information about the fading channel gains. In such a game-theoretic study, the central question is whether a Bayesian equilibrium exists, and if so, whether the network operates efficiently at the equilibrium point. We prove that there exists exactly one Bayesian equilibrium in our game. Furthermore, we study the network sum-rate maximization problem by assuming that the users coordinate according to a symmetric strategy profile. This result also serves as an upper bound for the Bayesian equilibrium. Finally, simulation results are provided to show the network efficiency at the unique Bayesian equilibrium and to compare it with other strategies.
Highlights
Fading multiple access channel (MAC) is a basic wireless channel model that allows several transmitters connected to the same receiver to transmit over it and share its capacity
By assuming that users compete with transmission rates as utility and transmit powers as moves, the authors show that there exists a unique Nash equilibrium [12] which corresponds to the maximum sum-rate point of the capacity region
The Bayesian equilibrium is unique in both cases, i.e., (0.6,0.6) and (0.5,0.5)
Summary
Fading multiple access channel (MAC) is a basic wireless channel model that allows several transmitters connected to the same receiver to transmit over it and share its capacity. The capacity region of fading MAC and the optimal resource allocation algorithms have been characterized and well studied in many pioneering works with different information assumptions [1]-[4]. By assuming that users compete with transmission rates as utility and transmit powers as moves, the authors show that there exists a unique Nash equilibrium [12] which corresponds to the maximum sum-rate point of the capacity region This claim is somewhat surprising, since in general Nash equilibrium is inefficient comparing to the Pareto optimality. As we previously pointed out, this assumption is rarely possible in practice This power allocation game needs to be reconstructed with some realistic assumptions made on the knowledge level of mobile devices.
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