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On the Convergence of Reinforcement Learning

  • Alan Beggs

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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File URL: http://www.economics.ox.ac.uk/materials/working_papers/paper96.pdf
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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 96.

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Date of creation: 01 Mar 2002
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Handle: RePEc:oxf:wpaper:96
Contact details of provider: Postal: Manor Rd. Building, Oxford, OX1 3UQ
Web page: http://www.economics.ox.ac.uk/
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  1. Ed Hopkins, 2001. "Two Competing Models of How People Learn in Games," Levine's Working Paper Archive 625018000000000226, David K. Levine.
  2. Sergiu Hart & Andreu Mas-Colell, 1999. "A General Class of Adaptive Strategies," Game Theory and Information 9904001, EconWPA, revised 23 Mar 2000.
  3. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
  4. J.-F. Laslier & R. Topol & B. Walliser, 1999. "A behavioral learning process in games," THEMA Working Papers 99-03, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  5. Rustichini, Aldo, 1999. "Optimal Properties of Stimulus--Response Learning Models," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 244-273, October.
  6. Arthur, W Brian, 1993. "On Designing Economic Agents That Behave Like Human Agents," Journal of Evolutionary Economics, Springer, vol. 3(1), pages 1-22, February.
  7. Tilman B�rgers & Rajiv Sarin, . "Learning Through Reinforcement and Replicator Dynamics," ELSE working papers 051, ESRC Centre on Economics Learning and Social Evolution.
  8. Josef Hofbauer & Karl H. Schlag, 2000. "Sophisticated imitation in cyclic games," Journal of Evolutionary Economics, Springer, vol. 10(5), pages 523-543.
  9. 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 848-81, September.
  10. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
  11. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  12. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
  13. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  14. Kuan, Chung-Ming & White, Halbert, 1994. "Adaptive Learning with Nonlinear Dynamics Driven by Dependent Processes," Econometrica, Econometric Society, vol. 62(5), pages 1087-1114, September.
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