Related papers: The convergence problem in mean field games with a…
We study a toy model of linear-quadratic mean field game with delay. We "lift" the delayed dynamic into an infinite dimensional space, and recast the mean field game system which is made of a forward Kolmogorov equation and a backward…
This work studies Nash equilibria for games where a mixture of coordinating and anti-coordinating agents, with possibly heterogeneous thresholds, coexist and interact through an all-to-all network. Whilst games with only coordinating or…
The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…
This paper is interested in the problem of optimal stopping in a mean field game context. The notion of mixed solution is introduced to solve the system of partial differential equations which models this kind of problem. This notion…
This paper proposes and studies a class of discrete-time finite-time-horizon Stackelberg mean-field games, with one leader and an infinite number of identical and indistinguishable followers. In this game, the objective of the leader is to…
We study a sequence of symmetric $n$-player stochastic differential games driven by both idiosyncratic and common sources of noise, in which players interact with each other through their empirical distribution. The unique Nash equilibrium…
This article introduces a class of $Nash$ games among $Stackelberg$ players ($NASPs$), namely, a class of simultaneous non-cooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a…
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…
Fictitious play (FP) is one of the most fundamental game-theoretical learning frameworks for computing Nash equilibrium in $n$-player games, which builds the foundation for modern multi-agent learning algorithms. Although FP has provable…
The goal of this paper is to show existence of short-time classical solutions to the so called Master Equation of \emph{first order} Mean Field Games, which can be thought of as the limit of the corresponding master equation of a stochastic…
In this paper we study a mean field control problem in which particles are absorbed when they reach the boundary of a smooth domain. The value of the N-particle problem is described by a hierarchy of Hamilton-Jacobi equations which are…
We study an optimal targeting problem for super-modular games with binary actions and finitely many players. The considered problem consists in the selection of a subset of players of minimum size such that, when the actions of these…
An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…
In this note, we study a class of deterministic finite-horizon linear-quadratic difference games with coupled affine inequality constraints involving both state and control variables. We show that the necessary conditions for the existence…
This work is mainly concerned with the so-called limit theory for mean-field games. Adopting the weak formulation paradigm put forward by Carmona and Lacker, we consider a fully non-Markovian setting allowing for drift control and…
This paper studies the problem of Nash equilibrium approximation in large-scale heterogeneous mean-field games under communication and computation constraints. A deterministic mean-field game is considered in which the non-linear utility…
The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game…
We study Markov perfect equilibria in continuous-time dynamic games with finitely many symmetric players. The corresponding Nash system reduces to the Nash-Lasry-Lions equation for the common value function, also known as the master…
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…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…