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This paper studies a linear-quadratic mean-field game of stochastic large-population system, where the large-population system satisfies a class of $N$ weakly coupled linear backward stochastic differential equation. Different from the…
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…
In this paper we establish quantitative convergence results for both open and closed-loop Nash equilibria of N-player stochastic differential games in the setting of Mean Field Games of Controls (MFGC), a class of models where interactions…
Structured game representations have recently attracted interest as models for multi-agent artificial intelligence scenarios, with rational behavior most commonly characterized by Nash equilibria. This paper presents efficient, exact…
Mean Field Games (MFG) have been introduced to tackle games with a large number of competing players. Considering the limit when the number of players is infinite, Nash equilibria are studied by considering the interaction of a typical…
This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum…
We formulate a class of mean field games on a finite state space with variational principles resembling those in continuous-state mean field games. We construct a controlled continuity equation featuring a nonlinear activation function on…
This letter studies multi-agent reinforcement learning in partially observable Markov potential games. Solving this problem is challenging due to partial observability, decentralized information, and the curse of dimensionality. First, to…
Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for…
The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…
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…
This paper is concerned with an indefinite linear-quadratic mean field games of stochastic large-population system, where the individual diffusion coefficients can depend on both the state and the control of the agents. Moreover, the…
In stochastic dynamical systems, different concepts of stability can be obtained in different limits. A particularly interesting example is evolutionary game theory, which is traditionally based on infinite populations, where strict Nash…
In this paper, we propose a graphon game model to understand how rumor (such as fake news) propagates in large populations that are interacting on a network and how different policies affect the spread. We extend the SKIR model that is used…
We consider stationary viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic mean-field game theory, and describe Nash equilibria of games with a large number of agents…
A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or…
Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not…
We study pure Nash equilibria in games on graphs with an imperfect monitoring based on a public signal. In such games, deviations and players responsible for those deviations can be hard to detect and track. We propose a generic epistemic…
The distributed computation of Nash equilibria is assuming growing relevance in engineering where such problems emerge in the context of distributed control. Accordingly, we present schemes for computing equilibria of two classes of static…
In this paper, we analyze mean-field game modulated by finite states markov chains. We first develop a sufficient stochastic maximum principle for the optimal control of a Markov-modulated stochastic differential equation (SDE) of…