Robust Additively Coupled Games in the Presence of Bounded Uncertainty in Communication Networks

We propose a novel scheme for robust communications in scenarios where channel gains, interference levels, or other measured values are uncertain or erroneously measured due to channel variations, delayed feedback, and users´ mobility. When the exact values of such measurements are known, it has been shown in the literature that multiuser wireless interactions can be modeled as additively coupled games (ACGs) in which users converge to a unique Nash equilibrium by following a distributed best-response algorithm. However, in practice, such measurements are uncertain or erroneous, and hence, it is important to analyze how these uncertainties and errors affect the performance of the users playing ACGs. Most importantly, novel adjustment schemes are needed to ensure that the utility of each user is preserved under such uncertainties, i.e., introduce robustness against uncertainties and errors in ACGs. We utilize the worst case robust optimization techniques to analyze the impact of uncertainties on the users´ performance and to build robust ACGs (RACGs). We derive sufficient conditions for the existence and uniqueness of their robust equilibrium and compare the outcome of an RACG and an ACG at their respective equilibria in terms of both utilities and the actions taken by the users. To reach the RACG´s equilibrium, we propose a novel distributed best-response algorithm and derive sufficient conditions for its convergence. Our analytical results are supported by simulations for power control games in interference channels and for flow control in Jackson networks.