Related papers: Learning Graphon Mean Field Games and Approximate …
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
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…
We consider a class of dynamic collective choice models with social interactions, whereby a large number of non-uniform agents have to individually settle on one of multiple discrete alternative choices, with the relevance of their would-be…
Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…
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…
We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a personal value…
We consider a system of $N$ particles whose interactions are characterized by a (weighted) graph $G^N$. Each particle is a node of the graph with an internal state. The state changes according to Markovian dynamics that depend on the states…
This paper addresses the problem of learning a Nash equilibrium in $\gamma$-discounted multiplayer general-sum Markov Games (MG). A key component of this model is the possibility for the players to either collaborate or team apart to…
We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the…
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…
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…
The aim of this paper is to study first order Mean field games subject to a linear controlled dynamics on $\mathbb R^{d}$. For this kind of problems, we define Nash equilibria (called Mean Field Games equilibria), as Borel probability…
This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior…
This paper proposes a distributed algorithm to find the Nash equilibrium in a class of non-cooperative convex games with partial-decision information. Our method employs a distributed projected gradient play approach alongside consensus…
The approximation of mixed Nash equilibria (MNE) for zero-sum games with mean-field interacting players has recently raised much interest in machine learning. In this paper we propose a mean-field gradient descent dynamics for finding the…
In this paper, we consider the problem of learning a generalized Nash equilibrium (GNE) in strongly monotone games. First, we propose a novel continuous-time solution algorithm that uses regular projections and first-order information. As…
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…
We analyse the typical structure of games in terms of the connectivity properties of their best-response graphs. Our central result shows that, among games that are `generic' (without indifferences) and that have a pure Nash equilibrium,…
We study distributed algorithms for seeking a Nash equilibrium in a class of non-cooperative convex games with strongly monotone mappings. Each player has access to her own smooth local cost function and can communicate to her neighbors in…
Linear quadratic graphon field games (LQ-GFGs) are defined to be LQ games which involve a large number of agents that are weakly coupled via a weighted undirected graph on which each node represents an agent. The links of the graph…