Chaotic and deterministic switching in a two-person game
AbstractWe study robust long-term complex behaviour in the Rock-Scissors-Paper game with two players, played using reinforcement learning. The complex behaviour is connected to the existence of a heteroclinic network for the dynamics. This network is made of three heteroclinic cycles consisting of nine equilibria and the trajectories connecting them. We provide analytical proof both for the existence of chaotic switching near the heteroclinic network and for the relative asymptotic stability of at least one cycle in the network, leading to behaviour ranging from almost deterministic actions to chaotic-like dynamics. Our results are obtained by making use of the symmetry of the original problem, a new approach in the context of learning.
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Bibliographic InfoPaper provided by Universidade do Porto, Faculdade de Economia do Porto in its series FEP Working Papers with number 305.
Length: 22 pages
Date of creation: Dec 2008
Date of revision:
learning process; dynamics; switching; chaos;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
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- Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
- Feltovich, Nick, 1999. "Equilibrium and reinforcement learning in private-information games: An experimental study1," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1605-1632, September.
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