相关论文: On non-uniqueness in mean field games

This paper is concerned with the study of mean field games master equations involving an additional variable modelling common noise. We address cases in which the dynamics of this variable can depend on the state of the game, which requires…

We consider mean field games with ergodic cost in the framework of a general discrete time controlled Markov processes. The state space of the processes is given by a general $\sigma$-compact Polish space. Under certain conditions, we show…

The paper is concerned with the study of a control system consisting of one major agent and many identical minor agents in the limit case when the number of agents tends to infinity. To study the limiting system we use the mean field…

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…

In this paper, we present a new development of inspection games in a mean field setting. In our dynamic version of an inspection game, there is one inspector and a large number N interacting inspectees with a finite state space. By applying…

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…

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…

We prove that solutions to a class of Mean Field Game systems with discount are unique provided that the discount factor is large enough, and the Lagrangian term is (proportionally) small enough. This identifies an asymptotic uniqueness…

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

We study optimal portfolio choice models in markets with partial information about the stock's drift. We solve the single agent problem for general utilities using a new approach that yields regularity of the value function and closed form…

Mean-payoff games on timed automata are played on the infinite weighted graph of configurations of priced timed automata between two players, Player Min and Player Max, by moving a token along the states of the graph to form an infinite…

We study a mean field game in continuous time over a finite horizon, T, where the state of each agent is binary and where players base their strategic decisions on two, possibly competing, factors: the willingness to align with the majority…

Mean field games allow to describe tractable models of dynamic games with a continuum of players, explicit interaction and heterogeneous states. Thus, these models are of great interest for socio-economic applications. A particular class of…

This paper studies a class of linear quadratic mean field games where the coefficients of quadratic cost functions depend on both the mean and the variance of the population's state distribution through its quantile function. Such a…

People, robots, and companies mostly divide time and effort among projects, and \defined{shared effort games} model people investing resources in public endeavors and sharing the generated values. In linear $\theta$ sharing (effort) games,…

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…

Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…

In this paper, we propose and study an inverse boundary problem for the mean field games (MFGs) governed by the first-order master equation in a bounded domain. We establish the unique identifiability result by showing that the running cost…

In this paper, we consider two-state mean-field games and its dual formulation. We then discuss numerical methods for these problems. Finally, we present various numerical experiments, exhibiting different behaviours, including shock…

We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…