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On the convergence of reinforcement learning

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  • Beggs, A.W.

Abstract

This paper examines the convergence of payoffs and strategies in Erev and Roth`s model of reinforcement learning. When all players use this rule it eliminates iteratively dominated strategies and in two-person constant-sum games average payoffs converge to the value of the game. Strategies converge in constant-sum games with unique equilibria if they are pure or in 2 × 2 games also if they are mixed. The long-run behaviour of the learning rule is governed by equations related to Maynard Smith`s version of the replicator dynamic. Properties of the learning rule against general opponents are also studied. In particular it is shown that it guarantees that the lim sup of a player`s average payoffs is at least his minmax payoff.
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Suggested Citation

  • Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
  • Handle: RePEc:eee:jetheo:v:122:y:2005:i:1:p:1-36
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    1. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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