Related papers: The master equation and the convergence problem in…
We consider a class of dynamic collective choice models with social interactions, whereby a large number of non-uniform agents have to individually settle on one of multiple discrete alternative choices, with the relevance of their would-be…
We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…
Mean-field games have been used as a theoretical tool to obtain an approximate Nash equilibrium for symmetric and anonymous $N$-player games. However, limiting applicability, existing theoretical results assume variations of a "population…
We study a class of dynamic decision problems of mean field type with time inconsistent cost functionals, and derive a stochastic maximum principle to characterize subgame perfect Nash equilibrium points. Subsequently, this approach is…
We investigate a time-inconsistent, non-Markovian finite-player game in continuous time, where each player's objective functional depends non-linearly on the expected value of the state process. As a result, the classical Bellman optimality…
We analyze the Master Equation within Mean Field Games (MFG) theory considering a bounded domain with homogeneous Dirichlet conditions. Concerning the N-players differential game, the player's dynamic ends when touching the boundary. We…
This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable…
We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…
In this paper we provide the existence of classical solutions to stationary mean field game systems in the whole space $\mathbb{R}^N$, with coercive potential and aggregating local coupling, under general conditions on the Hamiltonian. The…
We address the problem of regularity of solutions $u^i(t, x^1, \dots, x^N)$ to a family of semilinear parabolic systems of $N$ equations, which describe closed-loop equilibria of some $N$-player differential games with Lagrangian having…
This paper revisits the well-studied \emph{optimal stopping} problem but within the \emph{large-population} framework. In particular, two classes of optimal stopping problems are formulated by taking into account the \emph{relative…
We study a particular class of mean field games whose solutions can be formally connected to a scalar transport equation on the Wasserstein space of measures. For this class, we construct some interesting explicit examples of non-uniqueness…
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…
Nash`s classical bargaining solution suggests that n players in a non-cooperative bargaining situation should find a solution that maximizes the product of each player's utility functions. We consider a special case: Suppose that the…
We study Nash equilibria for a sequence of symmetric $N$-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative…
We analyze the behavior of a large number of strategic drivers traveling over an urban traffic network using the mean-field game framework. We assume an incentive mechanism for congestion mitigation under which each driver selecting a…
We investigate the set of Nash equilibrium payoffs for two person differential games. The main result of the paper is the characterization of the set of Nash equilibrium payoffs in the terms of nonsmooth analysis. Also we obtain the…
This article focuses two issues related to the first-order discounted mean field games system. The first is the time discretization problem. The time discretization approach enables us to prove the existence of solutions (u,m) of the…
Nash equilibria are crucial for understanding game behavior and systems in economics, physics, biology, and computer science. A significant application arises from the connection between Nash equilibria and optimization problems . However,…
We introduce and investigate certain $N$ player dynamic games on the line and in the plane that admit Coulomb gas dynamics as a Nash equilibrium. Most significantly, we find that the universal local limit of the equilibrium is sensitive to…