Skip to content
DraconiticResearch
Search Sources API
194,164 studies31 sourcesUpdated 31 min ago
PreprintarXiv licencearXiv

Detailed balance and phase transition in Nash equilibria of mean-field Ising game

  • Ken Hiura
  • Hajime Koike
  • Kiyoshi Kanazawa
Open at sourcePDFDOICite

Abstract

We study a finite-state mean-field game with entropic control cost. In the large population limit, we show that its stationary Nash equilibria satisfy the detailed balance condition and their distributions take the Gibbsian form with the value function playing the role of a Hamiltonian. We apply the entropic control cost to a ferromagnetic mean-field Ising game and investigate its stationary and non-stationary Nash equilibria. We find that the stationary Nash equilibria exhibit a second-order phase transition from disordered to ordered equilibria as temperature decreases. A center-manifold reduction yields non-stationary Nash equilibrium near the critical temperature and reveals the critical slowing down in the relaxation toward the stationary Nash equilibrium.

Related

  1. Phase transition in the antiferromagnetic Ising model with external field
    Jianping Jiang, Sike Lang
    arXivPreprintCC BY 4.0Full textMathematical physicsProbabilityarXiv
  2. Structure-Preserving Detailed-Balance Master-Equation Discretizations for Fokker--Planck Equations
    Satish Chandran, Yiwei Wang
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  3. Non-axisymmetric MHD equilibria with an arbitrary number of field periods
    Opal Issan, Lucas José, Matt Landreman +2
    arXivPreprintCC BY 4.0Full textMathematical physicsPlasma physicsarXiv
  4. Strategic Index Reconstitution: Differential Games, Closed-Loop Equilibria and Mean-Field Dynamics
    Lukas-Benedikt Fiechtner, Jose Blanchet
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  5. Beyond Nominal Equilibria: Risk-Averse Multi-Population Mean-Field Games
    Bhavini Jeloka, Siddhartha Ganguly, Panagiotis Tsiotras
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv

Cite

BibTeXRIS
BibTeX
@misc{hiura2026detailed,
  title = {{Detailed balance and phase transition in Nash equilibria of mean-field Ising game}},
  author = {Ken Hiura and Hajime Koike and Kiyoshi Kanazawa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36518},
  eprint = {2610.36518},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36518},
}
RIS
TY  - UNPB
TI  - Detailed balance and phase transition in Nash equilibria of mean-field Ising game
AU  - Ken Hiura
AU  - Hajime Koike
AU  - Kiyoshi Kanazawa
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36518
UR  - https://arxiv.org/abs/2610.36518
AB  - We study a finite-state mean-field game with entropic control cost. In the large population limit, we show that its stationary Nash equilibria satisfy the detailed balance condition and their distributions take the Gibbsian form with the value function playing the role of a Hamiltonian. We apply the entropic control cost to a ferromagnetic mean-field Ising game and investigate its stationary and non-stationary Nash equilibria. We find that the stationary Nash equilibria exhibit a second-order phase transition from disordered to ordered equilibria as temperature decreases. A center-manifold reduction yields non-stationary Nash equilibrium near the critical temperature and reveals the critical slowing down in the relaxation toward the stationary Nash equilibrium.
ER  -