Extended Graphon Mean-Field Games in Discrete Time
Abstract
In this paper, we study games involving a continuum of heterogeneous players in the discrete-time setting with finite state spaces and continuous action spaces. We introduce a new model that incorporates joint state-action interactions within the graphon-weighted aggregate, described by a coupled forward-backward system. We establish the existence of graphon mean-field equilibria and characterize them through this forward-backward system. Additionally, we provide uniqueness results under monotonicity and contraction conditions. To illustrate the practical relevance of our framework, we solve an example of portfolio liquidation with price impact. We provide numerical results for three different graphons and two different initial distributions, illustrating the impact of the network's structure and the distribution heterogeneity on the distribution and the policy.
Related
- Extended Mean Field Control Games with Moment Interactions: General Framework and Linear-Quadratic Model
- Optimization Frameworks & Learning Algorithms for Discrete-Time Mean Field Games
- Variational Contraction Conditions for Iterative Algorithms in Multi-Population Discrete-Time Regularized Mean-Field Games
- Convex ordering for graphon mean-field systems
- Mean-field quadratic BSDEs and related mean-field portfolio games of controls
BibTeX
@misc{amini2026extended,
title = {{Extended Graphon Mean-Field Games in Discrete Time}},
author = {Hamed Amini and Zhongyuan Cao and Gökçe Dayanıklı and Mathieu Laurière and Kexin Shao and Agnès Sulem},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04737},
eprint = {2609.04737},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05744476v1},
}
RIS
TY - UNPB
TI - Extended Graphon Mean-Field Games in Discrete Time
AU - Hamed Amini
AU - Zhongyuan Cao
AU - Gökçe Dayanıklı
AU - Mathieu Laurière
AU - Kexin Shao
AU - Agnès Sulem
PY - 2026
DA - 2026/09/04
PB - HAL
DO - 10.48550/arxiv.2609.04737
UR - https://hal.science/hal-05744476v1
AB - In this paper, we study games involving a continuum of heterogeneous players in the discrete-time setting with finite state spaces and continuous action spaces. We introduce a new model that incorporates joint state-action interactions within the graphon-weighted aggregate, described by a coupled forward-backward system. We establish the existence of graphon mean-field equilibria and characterize them through this forward-backward system. Additionally, we provide uniqueness results under monotonicity and contraction conditions. To illustrate the practical relevance of our framework, we solve an example of portfolio liquidation with price impact. We provide numerical results for three different graphons and two different initial distributions, illustrating the impact of the network's structure and the distribution heterogeneity on the distribution and the policy.
ER -