Related papers: Correlated equilibria and mean field games: a simp…
In the presence of a common noise, we study the convergence problems in mean field game (MFG) and mean field control (MFC) problem where the cost function and the state dynamics depend upon the joint conditional distribution of the…
The paper is concerned with two-person zero-sum mean-field linear-quadratic stochastic differential games over finite horizons. By a Hilbert space method, a necessary condition and a sufficient condition are derived for the existence of an…
This paper establishes an equilibrium existence result for a class of Mean Field Games involving Reflected Stochastic Differential Equations. The proof relies on the framework of relaxed controls and martingale problems.
We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available…
We establish the existence and uniqueness of a solution to the master equation for a mean field game of controls with absorption. The mean field game arises as a continuum limit of a dynamic game of exhaustible resources modeling Cournot…
Two-team zero-sum games are one of the most important paradigms in game theory. In this paper, we focus on finding an unexploitable equilibrium in large team games. An unexploitable equilibrium is a worst-case policy, where members in the…
We prove the existence of approximate correlated equilibrium of support size polylogarithmic in the number of players and the number of actions per player. In particular, using the probabilistic method, we show that there exists a multiset…
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…
This article examines mean-field-type game problems by means of a direct method. We provide various solvable examples beyond the classical linear-quadratic game problems. These include quadratic-quadratic games and games with power,…
We consider both $N$-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
A notion of incentive for agents is introduced which leads to a very general notion of an equilibrium for a finite game. Sufficient conditions for the existence of these equilibria are given. Known existence theorems are shown to be…
This paper considers a time-varying game with $N$ players. Every time slot, players observe their own random events and then take a control action. The events and control actions affect the individual utilities earned by each player. The…
The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…
The mean field games system is a coupled pair of nonlinear partial differential equations arising in differential game theory, as a limit as the number of agents tends to infinity. We prove existence and uniqueness of classical solutions…
Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…
This paper studies mean field game (MFG) of controls by featuring the joint distribution of the state and the control with the reflected state process along an exogenous stochastic reflection boundary. We contribute to the literature with a…
For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then,…
In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in…
This paper introduces a framework of Constrained Mean-Field Games (CMFGs), where each agent solves a constrained Markov decision process (CMDP). This formulation captures scenarios in which agents' strategies are subject to feasibility,…