## Tesi etd-05132017-001645 |

Thesis type

Tesi di dottorato di ricerca

Author

DE MATTEI, VALERIA

URN

etd-05132017-001645

Title

New approaches to Mean Field Game Theory

Settore scientifico disciplinare

MAT/06

Corso di studi

MATEMATICA

Commissione

**tutor**Prof. Flandoli, Franco

**commissario**Prof. Pratelli, Maurizio

**commissario**Prof. Morandin, Francesco

**commissario**Prof. Priola, Enrico

Parole chiave

- mean field game theory
- mean field
- moderate interactions
- mechanism design
- optimal control problem
- partial differential equation
- stochastic defferential equation

Data inizio appello

24/06/2017;

Consultabilità

completa

Riassunto analitico

The present thesis studies new possible approaches to Mean Field Game inspired by<br>Mechanism Design and Mean Field Theory with moderate interactions.<br>The structure of the thesis is the following.<br>The first part of the thesis studies mean field games in which the particles interact<br>like in mean field theory and in mean field theory with moderate interactions.<br>Chapter 2 studies competitions in which the agents interact in a mean field way<br>and convergence of the system to a proper mean field equation is proved. Chapter<br>3, starting from the ideas of chapter 2, consider the situation in which the agents<br>interact locally.<br>The second part of the thesis deals with the idea, inspired by Mechanism Design, of<br>introducing, in the context of mean field games, an external player, the Principal,<br>who can choose the rules of the game in order to achieve a specic outcome. Chapter<br>4 introduces the Principal in the context of classical mean field games; optimality<br>for the payoff of the Principal is studied. Chapter 5 consider the presence of the<br>Principal in the context of mean field games with mean field interactions: existence<br>of minimum for Principal's payoff is proved.

File

Nome file | Dimensione |
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PHD_DeMattei.pdf | 713.72 Kb |

report.pdf | 38.88 Kb |

sintesi.pdf | 16.63 Kb |

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