The present thesis studies new possible approaches to Mean Field Game inspired by Mechanism Design and Mean Field Theory with moderate inter- actions.
The structure of the thesis is the following.
The rst part of the thesis studies mean eld games in which the particles interact like in mean eld theory and in mean eld theory with moderate interactions. Chapter 2 studies competitions in which the agents interact in a mean eld way and convergence of the system to a proper mean eld equation is proved. Chapter 3, starting from the ideas of chapter 2, consider the situation in which the agents interact locally, as done by Oelschlager in the context of mean eld theory.
The second part of the thesis deals with the idea, inspired by Mechanism De- sign, of introducing, in the context of mean eld 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 clas- sical mean eld games; optimality for the payo of the Principal is studied.
Chapter 5 consider the presence of the Principal in the context of mean eld games with mean eld interactions: existence of minimum for Principal's payo is proved.
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