Related papers: Non-Asymptotic Mean-Field Games
In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinite-population limit of…
The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…
In this paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The main motivation for these considerations are the complex computations necessary to…
In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the…
In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of…
We introduce a mean-field term to an evolutionary spatial game model. Namely, we consider the game of Nowak and May, based on the Prisoner's dilemma, and augment the game rules by a self-consistent mean-field term. This way, an agent…
This article studies linear-quadratic Stackelberg games between two dominating players (or equivalently, leaders) and a large group of followers, each of whom interacts under a mean field game (MFG) framework. Unlike the conventional…
Mean Field Games with state constraints are differential games with infinitely many agents, each agent facing a constraint on his state. The aim of this paper is to provide a meaning of the PDE system associated with these games, the…
We present a novel framework for mean field games with finite state space and common noise, where the common noise is given through shocks that occur at random times. We first analyze the game for up to $n$ shocks, in which case we are able…
This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an…
In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of…
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,…
This paper investigates a novel class of mean field games involving a major agent and numerous minor agents, where the agents' functionals are recursive with nonlinear backward stochastic differential equation (BSDE) representations. We…
Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…
In this paper, we develop a Mean Field Games approach to Cluster Analysis. We consider a finite mixture model, given by a convex combination of probability density functions, to describe the given data set. We interpret a data point as an…
Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in…
A simple model of corruption that takes into account the effect of the interaction of a large number of agents by both rational decision making and myopic behavior is developed. Its stationary version turns out to be a rare example of an…
Mean field theory provides an effective way of scaling multiagent reinforcement learning algorithms to environments with many agents that can be abstracted by a virtual mean agent. In this paper, we extend mean field multiagent algorithms…
In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence and the uniqueness of equilibria of such games, we prove that…
Mean Field Game is a rather new field initially developed in applied mathematics and engineering in order to deal with the dynamics of a large number of controlled agents or objects in interaction. For a large class of these models, there…