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This paper provides a mathematical study of the well-posedness of master equation on finite state space involving terms modelling common noise. In this setting, the solution of the master equation depends on an additional variable modelling…
This paper considers a mean field game model inspired by crowd motion where agents want to leave a given bounded domain through a part of its boundary in minimal time. Each agent is free to move in any direction, but their maximal speed is…
The large-population system consists of considerable small agents whose individual behavior and mass effect are interrelated via their state-average. The mean-field game provides an efficient way to get the decentralized strategies of…
In this paper, we consider a first-order mean field game model motivated by crowd motion in which agents evolve in a (not necessarily compact) metric space and wish to reach a given target set. Each agent aims to minimize the sum of their…
Mean-field reinforcement learning (MF-RL) scales multi-agent RL to large populations by reducing each agent's dependence on others to a single summary statistic -- the mean action. However, this reduction requires every agent to act at…
We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a personal value…
Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most of the literature assumes a single initial distribution for the agents, which limits the practical applications of MFGs.…
In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an It\^o diffusion via one-sided singular stochastic control, aiming to…
Motivated by recent developments in mean-field games in ecology, in this paper we introduce a connection between the best response dynamics in evolutionary game theory, the minimization of the highest income of a game, and minimizing…
This paper addresses the decentralized coordinated charging problem for a large population of battery storage agents (e.g. residential batteries, electrical vehicles, charging station batteries) using Mean Field Game (MFG). Agents are…
This work solves the equilibrium price formation problem for the risky stock by combining mean-field game theory with the binomial tree framework, adapting the classic approach of Cox, Ross \& Rubinstein. For agents with exponential and…
Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other…
This paper studies multidimensional mean field games with common noise and the related system of McKean-Vlasov forward-backward stochastic differential equations deriving from the stochastic maximum principle. We first propose some…
We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE.…
We consider a model of nomadic agents exploring and competing for time-varying location-specific resources, arising in crowdsourced transportation services, online communities, and in traditional location based economic activity. This model…
The collective behaviour of stochastic multi-agents swarms driven by Gaussian and non-Gaussian environments is analytically discussed in a mean-field approach. We first exogenously implement long range mutual interactions rules with…
We consider a class of continuous-time dynamic games involving a large number of players. Each player selects actions from a finite set and evolves through a finite set of states. State transitions occur stochastically and depend on the…
We propose a new approach to mean field games with major and minor players. Our formulation involves a two player game where the optimization of the representative minor player is standard while the major player faces an optimization over…
This paper considers mean field games with optimal stopping time (OSMFGs) where agents make optimal exit decisions, the coupled obstacle and Fokker-Planck equations in such models pose challenges versus classic MFGs. This paper proposes a…
We consider a class of $N$-player games and mean-field games of singular controls with ergodic performance criterion, providing a benchmark case for irreversible investment games featuring mean-field interaction and strategic…