The school is devoted to three classes of problem: the generalized Nash equilibrium problems, the bilevel problems and the Mathematical Programming with Equilibrium Constraints. They interact through their mathematical analysis as well as their applications.
When dealing with noncooperative games, the classical concept of solution is the Nash equilibrium. However, in many game problems one encounters a situation where the strategy sets depend on the rival strategies. Such problems where termed as generalized Nash equilibrium problem (GNEP) and has applications in many fields like economics, pollution models, competitive network and wireless communication. This school will also emphasize on applications in electricity markets.
Whenever one of the agents is a leader of the market, the equilibrium problem turns out to be a bilevel problem. This is an optimization problem in whose the feasible region is the solution set of another optimization problem. Mathematical programming with equilibrium constraints (MPEC) is the study of constrained optimization problems where the constraints include variational inequalities and/or complementarities.
The main aim of the school is to present the modern tools of variational analysis and optimization used to analyse these three class of difficult problems. Applications and numerical approaches will play a central role in the proposed developments.