Introduction to the course (abstract):
Game theory is the study of mathematical models of conflict and cooperation between intelligent, rational decision-makers. Although its modern foundations were laid in economics and mathematics, game theory has since expanded far beyond its original scope. Today, it is increasingly adopted in engineering fields such as smart mobility, communication networks, energy grids, autonomous systems, and logistics. This course introduces core concepts and methods in non-cooperative game theory, including equilibrium concepts, existence and uniqueness results, dynamic and repeated interactions, and computational approaches based on convex analysis and monotone operator theory. Moreover, the course illustrates how these tools enable the modeling, analysis, and control of complex socio-technical systems, with applications ranging from energy and mobility infrastructures to autonomous systems.
Course content:
- Introduction to game theory (static, zero- and general-sum, potential games, pure strategies, mixed strategies);
- Equilibria definitions (Nash, Stackelberg, Wardrop, Generalized), existence and uniqueness results;
- Mathematical preliminaries of convex analysis (convex sets and functions, monotone operator theory);
- Numerical methods for the computation of equilibria in continuous games (best response, operator splitting methods, etc.);
- Dynamic games and game-theoretic control strategies;
- Population games and auctions;
- Application to modelling, analysis, and control of complex systems (electrical power grids, smart mobility, autonomous driving and racing);