Related papers: Forecasting Public Sentiments via Mean Field Games
We apply the generalized conditional gradient algorithm to potential mean field games and we show its well-posedeness. It turns out that this method can be interpreted as a learning method called fictitious play. More precisely, each step…
We show the convergence of finite state symmetric N-player differential games, where players control their transition rates from state to state, to a limiting dynamics given by a finite state Mean Field Game system made of two coupled…
We study mean field games and corresponding $N$-player games in continuous time over a finite time horizon where the position of each agent belongs to a finite state space. As opposed to previous works on finite state mean field games, we…
We introduce two algorithms based on a policy iteration method to numerically solve time-dependent Mean Field Game systems of partial differential equations with non-separable Hamiltonians. We prove the convergence of such algorithms in…
Recent algorithms allow decentralised agents, possibly connected via a communication network, to learn equilibria in mean-field games from a non-episodic run of the empirical system. However, these algorithms are for tabular settings: this…
We study convergence rates of the generalized conditional gradient (GCG) method applied to fully discretized Mean Field Games (MFG) systems. While explicit convergence rates of the GCG method have been established at the continuous PDE…
We generalize the notion of convexity and average-convexity to the notion of weighted average-convexity. We show several results on the relation between weighted average-convexity and cooperative games. First, we prove that if a game is…
This paper studies the connections between mean-field games and the social welfare optimization problems. We consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual…
Conventional Mean-field games/control study the behavior of a large number of rational agents moving in the Euclidean spaces. In this work, we explore the mean-field games on Riemannian manifolds. We formulate the mean-field game Nash…
The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…
This paper develops a linear programming approach for mean field games with reflected jump-diffusion dynamics. We first prove the equivalence between the mean field equilibria in the linear programming formulation and those in the weak…
This paper studies an optimal investment-consumption problem for competitive agents with exponential or power utilities and a common finite time horizon. Each agent regards the average of habit formation and wealth from all peers as…
We address the numerical solution of second-order Mean Field Game problems through Newton iterations in infinite dimensions, introduced in [14], where quadratic convergence of the method was rigorously established. Building upon this…
In this paper we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the…
We consider a class of Mean Field Games in which the agents may interact through the statistical distribution of their states and controls. It is supposed that the Hamiltonian behaves like a power of its arguments as they tend to infinity,…
In this paper, we introduce a bilevel optimization framework for addressing inverse mean-field games, alongside an exploration of numerical methods tailored for this bilevel problem. The primary benefit of our bilevel formulation lies in…
Precise and reliable climate projections are required for climate adaptation and mitigation, but Earth system models still exhibit great uncertainties. Several approaches have been developed to reduce the spread of climate projections and…
The only acceptable form of polling in the multi-billion dollar survey research field utilizes representative samples. We argue that with proper statistical adjustment, non-representative polling can provide accurate predictions, and often…
This paper studies the mean field game (MFG) problem arising from a large population competition in fund management, featuring a new type of relative performance via the benchmark tracking. In the $n$-player model, each agent aims to…
Several studies have shown that deep learning models can provide more accurate volatility forecasts than the traditional methods used within this domain. This paper presents a composite model that merges a deep learning approach with…