Pricing for distributed power control in multi-carrier systems

In this paper we consider the problem of data rate maximization of wireless users in multicarrier system in the context of game theory. In such a game, each user maximizes its data rate over all subcarriers while keeping its total transmit power bellow a given threshold. To control the selfish behavior of users we propose a new pricing mechanism whose value depends on transmit power of user as well as the channel condition of that user. We analyze the game, show that the game has Nash equilibrium (NE), provide conditions for the NE to be unique, and use an iteration algorithm to rich this unique NE. Using simulation we evaluate our proposed scheme and compare it to the case where pricing depends only on transmit power of user.