Chaos in learning a simple two-person game

Proceedings of the National Academy of Sciences of the United States of America
Yuzuru SatoJ Doyne Farmer

Abstract

We investigate the problem of learning to play the game of rock-paper-scissors. Each player attempts to improve her/his average score by adjusting the frequency of the three possible responses, using reinforcement learning. For the zero sum game the learning process displays Hamiltonian chaos. Thus, the learning trajectory can be simple or complex, depending on initial conditions. We also investigate the non-zero sum case and show that it can give rise to chaotic transients. This is, to our knowledge, the first demonstration of Hamiltonian chaos in learning a basic two-person game, extending earlier findings of chaotic attractors in dissipative systems. As we argue here, chaos provides an important self-consistency condition for determining when players will learn to behave as though they were fully rational. That chaos can occur in learning a simple game indicates one should use caution in assuming real people will learn to play a game according to a Nash equilibrium strategy.

References

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Citations

May 30, 2009·Bulletin of Mathematical Biology·Naoki Masuda, Hisashi Ohtsuki
Jan 9, 2013·Proceedings of the National Academy of Sciences of the United States of America·Tobias Galla, J Doyne Farmer
Dec 20, 2011·Cerebral Cortex·James DanckertBritt Anderson
Feb 27, 2013·PloS One·Seth Frey, Robert L Goldstone
Mar 13, 2014·Experimental Brain Research·Elisabeth StöttingerBritt Anderson
Aug 13, 2005·Brain Research. Cognitive Brain Research·Daeyeol LeeDominic J Barraclough
Aug 5, 2014·Current Biology : CB·Erman Misirlisoy, Patrick Haggard
Feb 18, 2014·Journal of Theoretical Biology·Naoki Masuda
Jan 18, 2017·Scientific Reports·Robin NicoleTobias Galla
Aug 16, 2011·Physical Review Letters·Daniele ViloneAngel Sánchez
Dec 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alex J Bladon, Tobias Galla
Jun 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ardeshir Kianercy, Aram Galstyan
Jul 11, 2019·Scientific Reports·Shayegan OmidshafieiRemi Munos
Aug 17, 2020·Physical Review. E·Riccardo Marcaccioli, Giacomo Livan
Mar 23, 2017·Scientific Reports·D BazeiaJ G G S Ramos
Mar 22, 2018·Scientific Reports·James B T SandersTobias Galla
Aug 25, 2004·Physical Review Letters·Arne TraulsenHeinz Georg Schuster
Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yuzuru Sato, James P Crutchfield
Nov 18, 2020·Journal of the Royal Society, Interface·Feng HuangLong Wang
Jan 1, 2021·Chaos·Archan Mukhopadhyay, Sagar Chakraborty
Dec 3, 2020·Chaos·Rohitashwa ChattopadhyaySagar Chakraborty
Jan 1, 2021·Chaos·Sergey DenisovMikhail Ivanchenko

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