Symmetry-breaking in a discrete-choice LQG mean field game
Abstract
Mean-field games provide a continuum framework for modeling the dynamics of large, interacting populations of non-cooperative agents. This paper studies symmetry-breaking in a finite-horizon, two-choice min-LQG mean-field game in which identical agents with linear stochastic dynamics choose one of two equally desirable terminal destinations, while trading off control effort against social pressure to conform. The model has an odd symmetry between the two destinations and therefore always admits a symmetric, dynamic Nash equilibrium in which the population splits evenly between them, producing a deadlock collective state at final time. Numerical studies have suggested that, as the penalty for social nonconformity increases, this symmetric equilibrium loses stability as a fixed point of an associated scalar, self-consistency map, and asymmetric consensus Nash equilibria emerge, where most agents select the same destination. By analyzing the linearized forward-backward PDE system through the scalar map representation, we provide a proof of this loss of stability of the symmetric equilibrium. Together with the odd symmetry of the map, this implies the existence of symmetry-broken mean-field game equilibria corresponding to consensus on either destination.
Related
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- Extended Graphon Mean-Field Games in Discrete Time
- Optimization Frameworks & Learning Algorithms for Discrete-Time Mean Field Games
- Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Data
- Symmetry and Rigidity Results for the Mean Field Equation and Hawking Mass on 𝕊2
BibTeX
@misc{lori2026symmetrybreaking,
title = {{Symmetry-breaking in a discrete-choice LQG mean field game}},
author = {Ali Akbar Rezaei Lori and Piyush Grover},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05730},
eprint = {2610.05730},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05730},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetry-breaking in a discrete-choice LQG mean field game
AU - Ali Akbar Rezaei Lori
AU - Piyush Grover
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.05730
UR - https://arxiv.org/abs/2610.05730
AB - Mean-field games provide a continuum framework for modeling the dynamics of large, interacting populations of non-cooperative agents. This paper studies symmetry-breaking in a finite-horizon, two-choice min-LQG mean-field game in which identical agents with linear stochastic dynamics choose one of two equally desirable terminal destinations, while trading off control effort against social pressure to conform. The model has an odd symmetry between the two destinations and therefore always admits a symmetric, dynamic Nash equilibrium in which the population splits evenly between them, producing a deadlock collective state at final time. Numerical studies have suggested that, as the penalty for social nonconformity increases, this symmetric equilibrium loses stability as a fixed point of an associated scalar, self-consistency map, and asymmetric consensus Nash equilibria emerge, where most agents select the same destination. By analyzing the linearized forward-backward PDE system through the scalar map representation, we provide a proof of this loss of stability of the symmetric equilibrium. Together with the odd symmetry of the map, this implies the existence of symmetry-broken mean-field game equilibria corresponding to consensus on either destination.
ER -