COARSE CORRELATED EQUILIBRIA IN CONTINUOUS-TIME MEAN FIELD GAMES
type: CreativeWork
description: Mean field games (MFGs), an active theme of research since the mid 2000's, arise as the limit formulation of symmetric N-player games with mean field interactions, and they act as a treatable approximation of such games, when the numbers of players is large enough. The usual notion of MFG solution can be regarded as the infinitely many players counterpart of the concept of Nash equilibrium in the underlying N-player game, and the connection between Nash equilibria and solutions to the MFG can be made rigorous via convergence arguments. The goal of this thesis is to introduce more general equilibria with better properties in continuous-time MFGs. In game theory literature, coarse correlated equilibria (CCEs) have been proposed as an alternative to Nash equilibria. CCEs can be seen as generalizations of the Nash equilibrium concept, incorporating a correlation device that allows agents to adopt correlated strategies without requiring cooperation. CCEs generalize Aumann's concept of correlated equilibria as well as Nash equilibria in both pure and mixed strategies. Among the nice features of CCEs, they are shown to be able to lead to higher payoffs than Nash equilibria in standard game theory, to be computationally ``easier'' and more natural to be learned by the players. In this thesis, we introduce CCEs in continuous-time MFGs and study their properties. In each chapter a different framework is considered and different problems are addressed, each requiring specific methodologies. In particular, the first chapter presents abstract results on the existence of CCEs in MFGs and on the approximation of CCEs in the underlying N-player games by means of the former ones. Subsequent chapters focus on detailed studies of specific MFG models, in which it is possible to analytically compute CCEs (or at least some of them) and compare them with more classical solution concepts. In Chapter 1 we consider MFGs driven by additive Wiener noise, with general drift and cost functions. …
abstract: Mean field games (MFGs), an active theme of research since the mid 2000's, arise as the limit formulation of symmetric N-player games with mean field interactions, and they act as a treatable approximation of such games, when the numbers of players is large enough. The usual notion of MFG solution can be regarded as the infinitely many players counterpart of the concept of Nash equilibrium in the underlying N-player game, and the connection between Nash equilibria and solutions to the MFG can be made rigorous via convergence arguments. The goal of this thesis is to introduce more general equilibria with better properties in continuous-time MFGs. In game theory literature, coarse correlated equilibria (CCEs) have been proposed as an alternative to Nash equilibria. CCEs can be seen as generalizations of the Nash equilibrium concept, incorporating a correlation device that allows agents to adopt correlated strategies without requiring cooperation. CCEs generalize Aumann's concept of correlated equilibria as well as Nash equilibria in both pure and mixed strategies. Among the nice features of CCEs, they are shown to be able to lead to higher payoffs than Nash equilibria in standard game theory, to be computationally ``easier'' and more natural to be learned by the players. In this thesis, we introduce CCEs in continuous-time MFGs and study their properties. In each chapter a different framework is considered and different problems are addressed, each requiring specific methodologies. In particular, the first chapter presents abstract results on the existence of CCEs in MFGs and on the approximation of CCEs in the underlying N-player games by means of the former ones. Subsequent chapters focus on detailed studies of specific MFG models, in which it is possible to analytically compute CCEs (or at least some of them) and compare them with more classical solution concepts. In Chapter 1 we consider MFGs driven by additive Wiener noise, with general drift and cost functions. …
author: CANNEROZZI, FEDERICO
language: eng
keywords: mean field game, stochastic differential game, coarse correlated equilibria, linear-quadratic model, singular control problems, Settore MATH-03/B - Probabilità e statistica matematica, Settore STAT-04/A - Metodi matematici dell'economia e delle scienze attuariali e finanziarie
date published: 2025-02-18
date modified: 2026-07-27T20:18:43Z
provider: Università degli Studi di Milano
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Università degli Studi di Milano

PropertyValue
property ID: Handle
value: https://hdl.handle.net/2434/1140335

PropertyValue
property ID: DOI
value: 10.13130/cannerozzi-federico_phd2025-02-18