Related papers: Dual two-state mean-field games

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if…

We present a new notion of solution for mean field games master equations. This notion allows us to work with solutions which are merely continuous. We prove first results of uniqueness and stability for such solutions. It turns out that…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

Here, we consider stationary monotone mean-field games (MFGs) and study the existence of weak solutions. First, we introduce a regularized problem that preserves the monotonicity. Next, using variational inequalities techniques, we prove…

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 examines mean-field-type game problems by means of a direct method. We provide various solvable examples beyond the classical linear-quadratic game problems. These include quadratic-quadratic games and games with power,…

Mean field Master equations for the norm game are investigated. The strategies are: to obey the norm or not and to punish those who break it or not. The punishment, the temptation, the punishment cost and the relaxation of vengeance are…

We present examples of equations arising in the theory of mean field games that can be reduced to a system in smaller dimensions. Such examples come up in certain applications, and they can be used as modeling tools to numerically…

We introduce a mean field game for a family of filtering problems related to the classic sequential testing of the drift of a Brownian motion. To the best of our knowledge this work presents the first treatment of mean field filtering games…

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…

We study the connection between the Aubry-Mather theory and a mean-field game (MFG) price-formation model. We introduce a framework for Mather measures that is suited for constrained time-dependent problems in R. Then, we propose a…

The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity…

We consider a mean-field game model where the cost functions depend on a fixed parameter, called \textit{state}, which is unknown to players. Players learn about the state from a a stream of private signals they receive throughout the game.…

A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton-Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption…

This paper investigates a linear-quadratic mean field games problem with common noise, where the drift term and diffusion term of individual state equations are coupled with both the state, control, and mean field terms of the state, and we…

Our aim is to model a game for power as a dynamical process, where an excess of power possessed by a player allows him to gain even more power. Such a positive feedback is often termed as the Matthew effect. Analytical and numerical methods…

Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to $+\infty$, have been introduced by J.-M. Lasry and P.-L. Lions. We use a change of variables to transform the…

We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…

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…