Lecturers: Antonio Marigonda (University of Verona) and Fabio Bagagiolo (University of Trento).
Period: March - April 2021.
Hours: 30 academic hours
Venue: the course will be delivered part in Trento and part in Verona, and a possible division of the arguments is (referring to the list below): arguments 1,2,3,8,9 in Verona (lecturer: Antonio Marigonda) and arguments 4,5,6,7,10 in Trento (lecturer: Fabio Bagagiolo). A streaming online connection between Trento and Verona will be organized.
Examiners: Antonio Marigonda and Fabio Bagagiolo.
Assessment Method: presentation of a survey on a topic treated in the course.
Scientific Sector: MAT/05 Analisi Matematica (Mathematical Analysis)
Contents: The differential games theory and the mean-field games theory are both concerned with the analytical mathematical treatment of strategic interactions between dynamical agents. This means that a number of agents/players may control their own dynamics in order to optimize some quantities that depend, among others, on the behaviour of all the other agents. Both theories rely on the optimal control theory, in particular for their dynamical feature. Optimal control theory is concerned with a single agent that has to optimize a cost depending only on its own actual state and control. Differential games are concerned with a finite number of agents (typically two), possibly in conflict with each other. Mean-field games are concerned with a very huge number of agents, possibly infinite, and the interaction between the agents is averaged and given by the so-called mean field. Typically, in game theory, one is interested in the study of possible equilibrium configurations. The motivations for this kind of studies are ubiquitous in the applications.
Prerequisites: differential and integral calculus in several variables, linear algebra, ordinary differential equations, uniform and weak convergence of functions, functional analysis, notions of partial differential equations, measure theory.
For more information, and instructions about enrolling, please visithttps://sites.google.com/unitn.it/phdcourse-control-maths-2021/home-page
Best regards,
Antonio Marigonda
