  We study the robust Nash equilibrium (RNE) for a class of games in
communications systems and networks where the impact of users on each other is
an additive function of their strategies. Each user measures this impact, which
may be corrupted by uncertainty in feedback delays, estimation errors,
movements of users, etc. To study the outcome of the game in which such
uncertainties are encountered, we utilize the worst-case robust optimization
theory. The existence and uniqueness conditions of RNE are derived using
finite-dimensions variational inequalities. To describe the effect of
uncertainty on the performance of the system, we use two criteria measured at
the RNE and at the equilibrium of the game without uncertainty. The first is
the difference between the respective social utility of users and, the second
is the differences between the strategies of users at their respective
equilibria. These differences are obtained for the case of a unique NE and
multiple NEs. To reach the RNE, we propose a distributed algorithm based on the
proximal response map and derive the conditions for its convergence.
Simulations of the power control game in interference channels, and Jackson
networks validate our analysis.
