## Thesis etd-05132017-001645 |

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Thesis type

Tesi di dottorato di ricerca

Author

DE MATTEI, VALERIA

URN

etd-05132017-001645

Thesis title

New approaches to Mean Field Game Theory

Academic discipline

MAT/06

Course of study

MATEMATICA

Supervisors

**tutor**Prof. Flandoli, Franco

**commissario**Prof. Pratelli, Maurizio

**commissario**Prof. Morandin, Francesco

**commissario**Prof. Priola, Enrico

Keywords

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

Graduation session start date

24/06/2017

Availability

Full

Summary

The present thesis studies new possible approaches to Mean Field Game inspired by

Mechanism Design and Mean Field Theory with moderate interactions.

The structure of the thesis is the following.

The first part of the thesis studies mean field games in which the particles interact

like in mean field theory and in mean field theory with moderate interactions.

Chapter 2 studies competitions in which the agents interact in a mean field way

and convergence of the system to a proper mean field equation is proved. Chapter

3, starting from the ideas of chapter 2, consider the situation in which the agents

interact locally.

The second part of the thesis deals with the idea, inspired by Mechanism Design, of

introducing, in the context of mean field games, an external player, the Principal,

who can choose the rules of the game in order to achieve a specic outcome. Chapter

4 introduces the Principal in the context of classical mean field games; optimality

for the payoff of the Principal is studied. Chapter 5 consider the presence of the

Principal in the context of mean field games with mean field interactions: existence

of minimum for Principal's payoff is proved.

Mechanism Design and Mean Field Theory with moderate interactions.

The structure of the thesis is the following.

The first part of the thesis studies mean field games in which the particles interact

like in mean field theory and in mean field theory with moderate interactions.

Chapter 2 studies competitions in which the agents interact in a mean field way

and convergence of the system to a proper mean field equation is proved. Chapter

3, starting from the ideas of chapter 2, consider the situation in which the agents

interact locally.

The second part of the thesis deals with the idea, inspired by Mechanism Design, of

introducing, in the context of mean field games, an external player, the Principal,

who can choose the rules of the game in order to achieve a specic outcome. Chapter

4 introduces the Principal in the context of classical mean field games; optimality

for the payoff of the Principal is studied. Chapter 5 consider the presence of the

Principal in the context of mean field games with mean field interactions: existence

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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