Robust Additively Coupled Games

We determine the robust Nash equilibrium (RNE) for a wide range of problems in communications systems and networks that are faced with uncertainty in their parameters’ values. This uncertainty can be caused by outdated measurements, estimation errors or limited information about other users present in the system. To define RNE, we utilize robust optimization techniques and focus on worst-case analysis. The existence and uniqueness conditions of RNE are derived using finite-dimension variational inequalities (VI). To understand the effect of uncertainty on the performance of the system, we define the difference between the achieved social utility at RNE and Nash equilibrium (NE) of the nominal game, and quantify this difference for the case when NE of the considered game is unique and also for the cases when the game has multiple NEs. We show that when the NE is unique, the achieved social utility at RNE is always less than that of the NE. Interestingly though, when multiple NEs e...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Saeedeh Parsaeefard, Ahmad R. Sharafat, Mihaela van der Schaar
• Keywords: CORR 2011, Education, Multiple Nes, Nash Equilibrium, Social Utility