  We consider private commons for secondary sharing of licensed spectrum bands
with no access coordination provided by the primary license holder. In such
environments, heterogeneity in demand patterns of the secondary users can lead
to constant changes in the interference levels, and thus can be a source of
volatility to the utilities of the users. In this paper, we consider secondary
users to be service providers that provide downlink services. We formulate the
spectrum sharing problem as a non-cooperative iterated game of power control
where service providers change their power levels to fix their long-term
average rates at utility-maximizing values. First, we show that in any iterated
2x2 game, the structure of the single-stage game dictates the degree of control
that a service provider can exert on the long-term outcome of the game. Then we
show that if service providers use binary actions either to access or not to
access the channel at any round of the game, then the long-term rate can be
fixed regardless of the strategy of the opponent. We identify these rates and
show that they can be achieved using mixed Markovian strategies that will be
clearly identified in the paper.
