Related papers: Mean-field interactions in evolutionary spatial ga…
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 introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players' states is described by a system of weakly interacting It\^o equations with…
Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate…
Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path…
We study some systems of interacting fields whose evolution is given by some singular stochastic partial differential equations of mean field type. We provide a robust setting for their study and prove a well-posedness result and a…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
Evolutionary games are a developing sub-field of game theory. This branch of game theory is used in the study of the adaptation of large, but finite, populations of agents to changes in the environment. It assumes that each agent has no…
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 a model of competition among nomadic agents for time-varying and location-specific resources, arising in crowd-sourced transportation services, online communities, and traditional location-based economic activity. This model…
A dynamic mean field theory is developed for finite state and action Bayesian reinforcement learning in the large state space limit. In an analogy with statistical physics, the Bellman equation is studied as a disordered dynamical system;…
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…
The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their…
We consider a mean field game describing the limit of a stochastic differential game of $N$-players whose state dynamics are subject to idiosyncratic and common noise and that can be absorbed when they hit a prescribed region of the state…
We study a class of linear-quadratic stochastic differential games in which each player interacts directly only with its nearest neighbors in a given graph. We find a semi-explicit Markovian equilibrium for any transitive graph, in terms of…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two…
We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…
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…
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent…
Photons mediate long-range optomechanical forces between atoms in high finesse resonators, which can induce the formation of ordered spatial patterns. When a transverse laser drives the atoms, the system undergoes a second order phase…