Opportunistic power allocation for fading channels with non-cooperative users and random access

We present a game-theoretical model of a wireless communication system with multiple competing users sharing a multi-access fading channel. With a specified capture rule and a limited amount of energy available, a user opportunistically adjusts its transmission power based on its own channel state to maximize the user´s own individual throughput. We derive an explicit form of the Nash equilibrium power allocation strategy. Furthermore, this Nash equilibrium power allocation strategy is unique under certain capture rule. We also quantify the loss of efficiency in throughput due to user´s selfish behavior. Moreover, as the number of users in the system increases, the total system throughput obtained by using a Nash equilibrium strategy approaches the maximum attainable throughput.