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A reinforcement learning process in extensive form games


  • Jean-François Laslier


  • Bernard Walliser



The CPR ("cumulative proportional reinforcement") learning rule stipulates that an agent chooses a move with a probability proportional to the cumulative payoff she obtained in the past with that move. Previously considered for strategies in normal form games (Laslier, Topol and Walliser, Games and Econ. Behav., 2001), the CPR rule is here adapted for actions in perfect information extensive form games. The paper shows that the action-based CPR process converges with probability one to the (unique) subgame perfect equilibrium.
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Suggested Citation

  • Jean-François Laslier & Bernard Walliser, 2005. "A reinforcement learning process in extensive form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 219-227, June.
  • Handle: RePEc:spr:jogath:v:33:y:2005:i:2:p:219-227 DOI: 10.1007/s001820400194

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    References listed on IDEAS

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    5. Peter Sudhölter & Bezalel Peleg, 2000. "The Positive Prekernel Of A Cooperative Game," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 287-305.
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    Cited by:

    1. Maxwell Pak & Bing Xu, 2016. "Generalized reinforcement learning in perfect-information games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 985-1011, November.
    2. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Gotts, Nicholas M. & Polhill, J. Gary, 2007. "Transient and asymptotic dynamics of reinforcement learning in games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 259-276, November.
    3. Thorsten Chmura & Thomas Pitz, 2007. "An Extended Reinforcement Algorithm for Estimation of Human Behaviour in Experimental Congestion Games," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(2), pages 1-1.
    4. Ioannou, Christos A. & Romero, Julian, 2014. "A generalized approach to belief learning in repeated games," Games and Economic Behavior, Elsevier, vol. 87(C), pages 178-203.
    5. Oyarzun, Carlos & Sarin, Rajiv, 2013. "Learning and risk aversion," Journal of Economic Theory, Elsevier, vol. 148(1), pages 196-225.
    6. Carlos Oyarzun & Rajiv Sarin, 2012. "Learning and Risk Aversion," Levine's Working Paper Archive 786969000000000572, David K. Levine.
    7. Schuster, Stephan, 2012. "Applications in Agent-Based Computational Economics," MPRA Paper 47201, University Library of Munich, Germany.


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