Related papers: Some remarks on Mean Field Games
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…
Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate…
In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for…
Finite mixture models are an important tool in the statistical analysis of data, for example in data clustering. The optimal parameters of a mixture model are usually computed by maximizing the log-likelihood functional via the…
We investigate large-scale effects induced by external fields, phenomenologically interpreted as mass media, in multiagent models evolving with the microscopic dynamics of the binary naming game. In particular, we show that a single…
In this paper, we consider a mean field game (MFG) with a major and $N$ minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional distribution in a nonlinear way. We use the stochastic…
We consider the mean-field game where each agent determines the optimal time to exit the game by solving an optimal stopping problem with reward function depending on the density of the state processes of agents still present in the game.…
We introduce a model of anonymous games with the player dependent action sets. We propose several learning procedures based on the well-known Fictitious Play and Online Mirror Descent and prove their convergence to equilibrium under the…
We consider a class of dynamic collective choice models with social interactions, whereby a large number of non-uniform agents have to individually settle on one of multiple discrete alternative choices, with the relevance of their would-be…
The goal of the paper is to develop the theory of finite state mean field games with major and minor players when the state space of the game is finite. We introduce the finite player games and derive a mean field game formulation in the…
We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution…
This note is concerned with a modeling question arising from the mean field games theory. We show how to model mean field games involving a major player which has a strategic advantage, while only allowing closed loop markovian strategies…
Mean field game equilibria are predicated on the assumption of immediate pairwise interactions within a population of homogeneous agents with asymptotically vanishing influence as population size increases. However, in many real-world…
In this paper, we consider a class of mean field games in which the optimal strategy of a representative agent depends on the statistical distribution of the states and controls. We prove some existence results for the forward-backward…
We study first order evolutive Mean Field Games whose operators are non-coercive. This situation occurs, for instance, when some directions are `forbidden' to the generic player at some points. Under some regularity assumptions, we…
We introduce a nonconvex Mean Field Games system by studying a model with a large number of identical pairs of players who are all rational, and each pair plays an identical zero-sum differential game. We study existence and uniqueness of…
We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…
In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish…
We study the dynamics and resulting score distribution of three-agent games where after each competition a single agent wins and scores a point. A single competition is described by a triplet of numbers $p$, $t$ and $q$ denoting the…
In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of…