Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm
- URL: http://arxiv.org/abs/2405.08005v2
- Date: Wed, 5 Jun 2024 02:51:23 GMT
- Title: Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm
- Authors: Fuzhong Zhou, Chenyu Zhang, Xu Chen, Xuan Di,
- Abstract summary: We prove the existence and uniqueness of the graphon equilibrium with mild assumptions, and show that this equilibrium can be used to construct an approximate solution for finite player game on networks.
An online oracle-free learning algorithm is developed to solve the equilibrium numerically, and sample complexity analysis is provided for its convergence.
- Score: 14.647775453098513
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both philosophical and mathematical advantages, compared to a widely adopted formulation using a continuum of players. We prove the existence and uniqueness of the graphon equilibrium with mild assumptions, and show that this equilibrium can be used to construct an approximate solution for finite player game on networks, which is challenging to analyze and solve due to curse of dimensionality. An online oracle-free learning algorithm is developed to solve the equilibrium numerically, and sample complexity analysis is provided for its convergence.
Related papers
- Nash Equilibria via Stochastic Eigendecomposition [4.190518009892366]
We show a Nash equilibrium can be approximated with purely calls to parameter, iterative variants of value decomposition and power.
We provide pseudocode and experiments demonstrating solving for all equilibria of a general-sum game using only readily available linear algebra tools.
arXiv Detail & Related papers (2024-11-04T17:32:21Z) - Last-Iterate Convergence of Payoff-Based Independent Learning in Zero-Sum Stochastic Games [31.554420227087043]
We develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players.
In the matrix game setting, the results imply a complexity of $O(epsilon-1)$ to find the Nash distribution.
In the game setting, the results also imply a complexity of $O(epsilon-8)$ to find a Nash equilibrium.
arXiv Detail & Related papers (2024-09-02T20:07:25Z) - Neural Population Learning beyond Symmetric Zero-sum Games [52.20454809055356]
We introduce NeuPL-JPSRO, a neural population learning algorithm that benefits from transfer learning of skills and converges to a Coarse Correlated (CCE) of the game.
Our work shows that equilibrium convergent population learning can be implemented at scale and in generality.
arXiv Detail & Related papers (2024-01-10T12:56:24Z) - On the Convergence of No-Regret Learning Dynamics in Time-Varying Games [89.96815099996132]
We characterize the convergence of optimistic gradient descent (OGD) in time-varying games.
Our framework yields sharp convergence bounds for the equilibrium gap of OGD in zero-sum games.
We also provide new insights on dynamic regret guarantees in static games.
arXiv Detail & Related papers (2023-01-26T17:25:45Z) - Finding mixed-strategy equilibria of continuous-action games without
gradients using randomized policy networks [83.28949556413717]
We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients.
We model players' strategies using artificial neural networks.
This paper is the first to solve general continuous-action games with unrestricted mixed strategies and without any gradient information.
arXiv Detail & Related papers (2022-11-29T05:16:41Z) - Learning Correlated Equilibria in Mean-Field Games [62.14589406821103]
We develop the concepts of Mean-Field correlated and coarse-correlated equilibria.
We show that they can be efficiently learnt in emphall games, without requiring any additional assumption on the structure of the game.
arXiv Detail & Related papers (2022-08-22T08:31:46Z) - A unified stochastic approximation framework for learning in games [82.74514886461257]
We develop a flexible approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite)
The proposed analysis template incorporates a wide array of popular learning algorithms, including gradient-based methods, exponential/multiplicative weights for learning in finite games, optimistic and bandit variants of the above, etc.
arXiv Detail & Related papers (2022-06-08T14:30:38Z) - Multiplayer Performative Prediction: Learning in Decision-Dependent
Games [18.386569111954213]
This paper formulates a new game theoretic framework for multi-player performative prediction.
We focus on two distinct solution concepts, namely (i) performatively stable equilibria and (ii) Nash equilibria of the game.
We show that under mild assumptions, the performatively stable equilibria can be found efficiently by a variety of algorithms.
arXiv Detail & Related papers (2022-01-10T15:31:10Z) - Learning Graphon Mean Field Games and Approximate Nash Equilibria [33.77849245250632]
We propose a novel discrete-time formulation for graphon mean field games with weak interaction.
On the theoretical side, we give extensive and rigorous existence and approximation properties of the graphon mean field solution.
We successfully obtain plausible approximate Nash equilibria in otherwise infeasible large dense graph games with many agents.
arXiv Detail & Related papers (2021-11-29T16:16:11Z) - Sample-Efficient Learning of Stackelberg Equilibria in General-Sum Games [78.65798135008419]
It remains vastly open how to learn the Stackelberg equilibrium in general-sum games efficiently from samples.
This paper initiates the theoretical study of sample-efficient learning of the Stackelberg equilibrium in two-player turn-based general-sum games.
arXiv Detail & Related papers (2021-02-23T05:11:07Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.