A Game of Uncoordinated Sharing of Private Spectrum Commons

We consider secondary provisioning of radio spectrum where usage rights of a wireless channel are granted to secondary users without necessarily relying on the network of the primary license holder. In return, the secondary users pay the license holder per unit data transmitted on the channel. The rates that the secondary users achieve depend on the interference they create to each other, which also can vary temporally based on the activities of the users on the channel. In this work, channel sharing is considered from the standpoint of a user that aims at fixing its long-term average rate at a utility maximizing value, without the need for predicting the behavior of other users. The problem is formulated as a non-cooperative game of channel access played in rounds, where, in each round, a user decides whether or not to access the channel based on the outcome of the game in the previous round. The single round payoff matrix of the channel access game of two users is shown in Figure 1. In each round, the users choose from a binary action space to transmit at a certain power level or at zero power. If one user accesses the channel, it will achieve rate R1 for user 1 or R2 for user 2. However, if the two users access the channel concurrently, they both achieve lower rates with 0 < θ1, θ2 < 1.