Related papers: Iterative Schemes for Markov Perfect Equilibria
A model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered. The asymmetry of information…
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…
In this paper, we study the well-posedness (existence and uniqueness) of the Master Equation of Mean Field Games under invariance-type conditions, otherwise known as viability conditions for the controlled dynamics. The interior regularity…
The purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games for which the interaction between the players is of mean-field type. We implement the Mean-Field Games strategy…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
We consider graphical $n$-person games with perfect information that have no Nash equilibria in pure stationary strategies. Solving these games in mixed strategies, we introduce probabilistic distributions in all non-terminal positions. The…
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…
For a class of finite horizon first order mean field games and associated N-player games, we give a simple proof of convergence of symmetric N-player Nash equilibria in distributed open-loop strategies to solutions of the mean field game in…
Mean field games model equilibria in games with a continuum of players as limiting systems of symmetric $n$-player games with weak interaction between the players. We consider a finite-state, infinite-horizon problem with two cost criteria:…
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…
In this study, we investigate $N$-player stochastic differential games with regime switching, where the player dynamics are modulated by a finite-state Markov chain. We analyze the associated Nash system, which consists of a system of…
We propose a reinforcement learning algorithm for stationary mean-field games, where the goal is to learn a pair of mean-field state and stationary policy that constitutes the Nash equilibrium. When viewing the mean-field state and the…
In this paper we present a novel generic mapping between Graphical Games and Markov Random Fields so that pure Nash equilibria in the former can be found by statistical inference on the latter. Thus, the problem of deciding whether a…
We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…
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 (MFGs) model equilibria in games with a continuum of weakly interacting players as limiting systems of symmetric $n$-player games. We consider the finite-state, infinite-horizon problem with ergodic cost. Assuming Markovian…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
Computing Nash equilibrium policies is a central problem in multi-agent reinforcement learning that has received extensive attention both in theory and in practice. However, provable guarantees have been thus far either limited to fully…
This paper presents a novel data-driven approach for approximating the $\varepsilon$-Nash equilibrium in continuous-time linear quadratic Gaussian (LQG) games, where multiple agents interact with each other through their dynamics and…
We present a framework for computing approximate mixed-strategy Nash equilibria of continuous-action games. It is a modification of the traditional double oracle algorithm, extended to multiple players and continuous action spaces. Unlike…