Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Chaos in learning a simple two-person game.

Yuzuru Sato1, Eizo Akiyama, J Doyne Farmer

  • 1Brain Science Institute, The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan. ysato@bdc.riken.go.jp

Proceedings of the National Academy of Sciences of the United States of America
|April 4, 2002
PubMed
Summary

This study demonstrates Hamiltonian chaos in rock-paper-scissors learning. Chaos in simple games suggests caution when assuming players reach Nash equilibrium strategies.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Chaotic stochastic resonance in Mackey-Glass equations.

Chaos (Woodbury, N.Y.)·2026
Same author

Noise-induced transitions in random Pomeau-Manneville maps.

Chaos (Woodbury, N.Y.)·2025
Same author

El Niño and droughts in Southeast Asia: A stochastic-chaotic modeling approach.

Physical review. E·2025
Same author

Supply and demand shocks in the COVID-19 pandemic: an industry and occupation perspective.

Oxford review of economic policy·2025
Same author

Transition to anomalous dynamics in a simple random map.

Chaos (Woodbury, N.Y.)·2024
Same author

The unequal effects of the health-economy trade-off during the COVID-19 pandemic.

Nature human behaviour·2023

Area of Science:

  • Game Theory
  • Computational Economics
  • Chaos Theory

Background:

  • Reinforcement learning models player adaptation.
  • Previous research identified chaotic attractors in dissipative systems.

Purpose of the Study:

  • Investigate learning dynamics in rock-paper-scissors.
  • Demonstrate Hamiltonian chaos in a basic two-person game.
  • Analyze learning behavior and rationality conditions.

Main Methods:

  • Utilized reinforcement learning to model player strategy adjustment.
  • Examined both zero-sum and non-zero-sum game scenarios.
  • Analyzed learning trajectories and their dependence on initial conditions.

Main Results:

Related Experiment Videos

  • The zero-sum game learning process exhibits Hamiltonian chaos.
  • Learning trajectories can be simple or complex, influenced by initial conditions.
  • The non-zero-sum case can lead to chaotic transients.

Conclusions:

  • This is the first demonstration of Hamiltonian chaos in learning a basic two-person game.
  • Chaos acts as a self-consistency condition for rational player behavior.
  • Caution is advised when assuming real players will learn Nash equilibrium strategies.