DESCRIPTION. In the Mean Field Games models, in the view of an optimization criterion, many (even infinitely many) agents individually take their 
decisions, being anyway 
influenced by the behavior of all other agents. Each single agent has only the perception of the average behavior of the others. This fact brings to a limit model 
given by two partial differential equations: one (Hamilton-Jacobi) for the optimal behavior of the single agent, the other one (transport, Fokker-Planck) for the 
evolution of the distribution of the population. MFG is a recent subject of research and may suitably describe: crowd/opinion/electrical grid dynamics, financial 
markets, and many others. The argument of the thesis can be cut on more mathematical aspects or on more applicative aspects.

<br>

MATHEMATICAL TOPICS AND SOME REFERENCES: Optimal control problems: Dynamic Programming and Hamilton-Jacobi equations. Transport equations and conservation laws.  
Equilibrium in non-cooperative games. Weak solutions of partial differential equations.
<li>
M. Bardi & I. Capuzzo Dolcetta: Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhauser, 1997
</li>
<li>
A. Bressan: Noncooperative Differential Games: a Tutorial (from the website of the author)
</li>
<li>
P. Cardaliaguet: Notes on Mean Field Games (from the website of the author)
</li>
<li>
L. C. Evans: Partial Differential Equations, AMS, 1998.
</li>