**Venue**: Seminar Room "-1" - Department of Mathematics – Via Sommarive, 14 - Povo Trento

**Hour**: 3.30 p.m.

**Benatti Luca** - PhD in Mathematics

**Abstract**:

A sharp idea in mean field games theory is that the mean field, which is the distribution of choices for an infinite number of players, is somehow related with Nash equilibrium in games with ?? agents for ???+8. The study of finite games is, therefore, the first step to study this kind of problem.

Without any further assumption, the growth of the number of players may lead to an increase in complexity. Payoff functions, functions that each agent want to minimize, are different from a player to another. The requirement that each player is undistinguishable can be translated in the fact that payoff functions are defined on the same set of choices and are in some sense symmetric. In this talk, we want to present how this requirement can be used to simplify the problem and to study the evolution of Nash equilibria in the limit problem.

*The seminar corresponds to the exam of the first part of “Mean Field Games and Optimal Transport”, a planned course within Benatti's first year PHD study programme *

Contact person: **Fabio Bagagiolo**