  This paper considers non-cooperative and fully-distributed power-allocation
for secondary-users (SUs) in spectrum-sharing environments when
normalized-interference to each secondary-user is uncertain. We model each
uncertain parameter by the sum of its nominal (estimated) value and a bounded
additive error in a convex set, and show that the allocated power always
converges to its equilibrium, called robust Nash equilibrium (RNE). In the case
of a bounded and symmetric uncertainty set, we show that the power allocation
problem for each SU is simplified, and can be solved in a distributed manner.
We derive the conditions for RNE's uniqueness and for convergence of the
distributed algorithm; and show that the total throughput (social utility) is
less than that at NE when RNE is unique. We also show that for multiple RNEs,
the the social utility may be higher at a RNE as compared to that at the
corresponding NE, and demonstrate that this is caused by SUs' orthogonal
utilization of bandwidth for increasing the social utility. Simulations confirm
our analysis.
