Abstract
We consider a wireless collision channel, shared by a finite number of mobile users who transmit to a common base station using a random access protocol. Mobiles are self-optimizing, and wish to minimize their individual average power investment subject to minimum-throughput demand. The channel state between each mobile and the base station is stochastically time-varying and is observed by the mobile prior to transmission. Given the current channel state, a mobile may decide whether to transmit or not, and to determine the transmission power in case of transmission. In this paper, we investigate the properties of the Nash equilibrium of the resulting game in multiuser networks. We characterize the best-response strategy of the mobile and show that it leads to a "water-filling"-like power allocation. Our equilibrium analysis then reveals that one of the possible equilibria is uniformly best for all mobiles. Furthermore, this equilibrium can be reached by a simple distributed mechanism that does not require specific information on other mobiles' actions. We then explore some additional characteristics of the distributed power control framework. Braess-like paradoxes are reported, where the use of multiple power levels can diminish system capacity and also lead to larger per-user power consumption, compared to the case where a single level only is permitted.
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