Related papers: Mean Field Games Incorporating Carryover Effects: …
We exhibit optimal control strategies for a simple toy problem in which the underlying dynamics depend on a parameter that is initially unknown and must be learned. We consider a cost function posed over a finite time interval, in contrast…
The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…
Mean field games (MFGs) offer a versatile framework for modeling large-scale interactive systems across multiple domains. This paper builds upon a previous work, by developing a state-of-the-art unified approach to decode or design the…
Mean Field Game is a rather new field initially developed in applied mathematics and engineering in order to deal with the dynamics of a large number of controlled agents or objects in interaction. For a large class of these models, there…
The use of game theoretic methods for control in multiagent systems has been an important topic in recent research. Valid utility games in particular have been used to model real-world problems; such games have the convenient property that…
We propose a new approach to proving the uniqueness of solutions to a certain class of mean field games of controls. In this class, the equilibrium is determined by an aggregate quantity $Q(t)$, e.g. the market price or production, which…
While the general theory for the terminal-initial value problem in mean-field games is widely used in many models of applied mathematics, the modeling potential of the corresponding forward-forward version is still under-considered. In this…
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…
This paper studies a mean field game inspired by crowd motion in which agents evolve in a compact domain and want to reach its boundary minimizing the sum of their travel time and a given boundary cost. Interactions between agents occur…
We investigate infinite games on finite graphs where the information flow is perturbed by nondeterministic signalling delays. It is known that such perturbations make synthesis problems virtually unsolvable, in the general case. On the…
This paper studies social optimal control of mean field LQG (linear-quadratic-Gaussian) models with uncertainty. Specially, the uncertainty is represented by a uncertain drift which is common for all agents. A robust optimization approach…
This paper focuses on a model for opinion dynamics, where the influence weights of agents evolve in time. We formulate a control problem of consensus type, in which the objective is to drive all agents to a final target point under suitable…
In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…
We consider a data-driven formulation of the classical discrete-time stochastic control problem. Our approach exploits the natural structure of many such problems, in which significant portions of the system are uncontrolled. Employing the…
In this paper we study optimal advertising problems that models the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we…
We consider the problem of devising incentive strategies for viral marketing of a product. In particular, we assume that the seller can influence penetration of the product by offering two incentive programs: a) direct incentives to…
We consider a finite number of $N$ statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on…
Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we…
We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish…