ETD system

Electronic theses and dissertations repository

 

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&#39;s payoff is proved.
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