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We consider private commons for secondary sharing of licensed spectrum bandswith no access coordination provided by the primary license holder. In suchenvironments, heterogeneity in demand patterns of the secondary users can leadto constant changes in the interference levels, and thus can be a source ofvolatility to the utilities of the users. In this paper, we consider secondaryusers to be service providers that provide downlink services. We formulate thespectrum sharing problem as a non-cooperative iterated game of power controlwhere service providers change their power levels to fix their long-termaverage rates at utility-maximizing values. First, we show that in any iterated2x2 game, the structure of the single-stage game dictates the degree of controlthat a service provider can exert on the long-term outcome of the game. Then weshow that if service providers use binary actions either to access or not toaccess the channel at any round of the game, then the long-term rate can befixed regardless of the strategy of the opponent. We identify these rates andshow that they can be achieved using mixed Markovian strategies that will beclearly identified in the paper.

An Iterated Game of Uncoordinated Sharing of Licensed Spectrum Using Zero-Determinant Strategies