We consider continuous-kernel games with shared coupled constraints and the problem of how to distributively find an equilibrium solution, namely a variational generalized Nash equilibrium (GNE). We show how, based on a variational inequality characterization and the KKT conditions, this can be reformulated as how to find zeros of a sum of monotone operators. Based on this, GNE seeking algorithms can be developed via operator-splitting methods, guaranteed to globally converge with fixed step-sizes under perfect information on the other players’ decisions. We consider how to distribute such algorithms in partial-information settings over networks, where players can only communicate with their neighbours, while their costs depend on everyone else’s decision. To distribute the problem, we augment variables, so that each player has local decision estimates and local copies of Lagrangian multipliers. We then show how the problem can be recast as a zero-finding problem for a sum of appropriately augmented monotone operators, with a special preconditioning matrix. Extensions to asynchronous and/or aggregative regimes can be treated within the same operator theoretic framework.
Lacra Pavel is a professor in the Systems Control group, Department of Electrical and Computer Engineering, University of Toronto, Canada. She received the Diploma of Engineer in Automatic Control from Technical University of Iasi, Romania, and the Ph.D. degree in Electrical Engineering from Queen's University at Kingston, Canada in 1996. She joined University of Toronto in August 2002, after a postdoctoral stage at the National Research Council and four years of working in the industry. Her research interests are in game theory and distributed optimization in networks, with emphasis on system control aspects. She is the author of the book "Game Theory for Control of Optical Networks" (Birkhauser-Springer Science). She acted as Publications Chair of the 45th IEEE Conference on Decision and Control and is currently an Associate Editor for the IEEE CSS Conference Editorial Board and IEEE Transactions on Control of Network Systems.