Related papers: Discrete potential mean field games: duality and n…
We propose an efficient solution approach for high-dimensional nonlocal mean-field game (MFG) systems based on the Monte Carlo approximation of interaction kernels via random features. We avoid costly space-discretizations of interaction…
This paper studies mean field games for multi-agent systems with control-dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal…
In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players' states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints,…
This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…
Mean field games (MFGs) describe the collective behavior of large populations of interacting agents. In this work, we tackle ill-posed inverse problems in potential MFGs, aiming to recover the agents' population, momentum, and environmental…
We extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian,…
We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In Stackelberg MFG, an infinite population of agents play a non-cooperative game and choose their controls to optimize their individual…
We propose a new class of games, called Multi-Games (MG), in which a given number of players play a fixed number of basic games simultaneously. In each round of the MG, each player will have a specific set of weights, one for each basic…
In this paper we study a mean field model for discrete time, finite number of states, dynamic games. These models arise in situations that involve a very large number of agents moving from state to state according to certain optimality…
Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this context, we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of a MFG equilibrium with the minimal cost a global…
We study a particle approximation for one-dimensional first-order Mean-Field-Games (MFGs) with local interactions with planning conditions. Our problem comprises a system of a Hamilton-Jacobi equation coupled with a transport equation. As…
Synthesizing near-optimal mixed strategies for zero-sum differential games (ZSDGs) has been a longstanding challenge. Existing research mainly focuses on characterizing the theoretical value function, while the practical design of…
We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…
First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results…
In this article, we propose two numerical methods, the Gaussian Process (GP) method and the Fourier Features (FF) algorithm, to solve mean field games (MFGs). The GP algorithm approximates the solution of a MFG with maximum a posteriori…
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…
We develop the linear programming approach to mean-field games in a general setting. This relaxed control approach allows to prove existence results under weak assumptions, and lends itself well to numerical implementation. We consider…
The theory of first-order mean field type differential games examines the systems of infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study the…
This paper studies efficient distributed optimization methods for multi-agent networks. Specifically, we consider a convex optimization problem with a globally coupled linear equality constraint and local polyhedra constraints, and develop…
This paper introduces a new method based on Deep Galerkin Methods (DGMs) for solving high-dimensional stochastic Mean Field Games (MFGs). We achieve this by using two neural networks to approximate the unknown solutions of the MFG system…