France Canada Research Fund

New Scientific Collaboration Support Program:

Project title: Novel results on generalized Nash games and their links to AI

Highlights: The team and HQP propose to study the links between generalized Nash games, nonsmooth dynamics and AI tecniques useful for identifying/analyzing general Nash equilibria. The concept of Nash equilibrium was introduced by John F. Nash in 1950, preceded by A. Cournot in 1838, who anticipated the idea in his analysis of competition between two companies. The conditions for the existence of a Nash equilibrium are mathematically based on fixed point theorems, and it is possible in some games to obtain several Nash equilibria. The question then arises which one is the most reasonable. With the emergence of AI problems, game theory can be used in many machine learning models. This is the case for example of classification algorithms such as SVM (Support Vector Machines) that can be explained as a two-player game. The Nash equilibrium translates that the players agree that there exists no better solution and none of the players would have any benefit in modifying their current strategies. In the context of SVM, the NE is reached when the SVM classifier fixes the hyperplane to use for classifying the data. This project proposes to expand and bridge the use of AI together with game theoretic tools to answer possible selection issues in generalized Nash games.

Canadian Lead (team): background and expertise:

Monica Cojocaru has worked on mathematical research in the area of equilibrium problems, game theory and dynamical systems. She studied equilibrium problems, which concern themselves with the mathematical modelling of economic (Wardrop), game theoretic (Nash), and physical equilibria. She is best known for her results on existence and qualitative behaviour of equilibrium points of classes of equilibrium problems (see [C5] (IF 3.8) and [C6]). Recently she developed new results in the area of generalized Nash games. (Team members: L. Humphrey, R. Fields - M. Sc., M. Nahirniak, Ph. D., D. Flynn-Primrose - PDF)

French Lead (team): background and expertise

Samir Adly (SA) received an M.Sc. in Mathematics (1992) and a Ph.D. in Applied Mathematics (1995), both from the University of Limoges (France). In 1997 he became Associate Professor and in 2006 full Professor of Mathematics at University of Limoges. His research interests focus on theoretical and algorithmic issues related to variational inequalities, complementarity problems, optimization, nonsmooth dynamical systems. He is Director of the Mathematics and Computer Science Department of the Institute of Research XLIM (UMR-CNRS 7252). He is Director of the CNRS Group of Research: Mathematics of Optimization and Applications (GdR MOA N 3273): http://gdrmoa.math.cnrs.fr. He is Head of MOD "Modeling, Optimization, Dynamics" of the department of Mathematics and is the founder of the Master degree ACSYON. (Team members: Nguyen Van Nam, Ph. D. and 1 M. Sc. student)