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Rule Learning in Symmetric Normal-Form Games: Theory and Evidence

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  • Dale O. Stahl

    ()
    (Eco, U. of Texas)

Abstract

We improve Stahl's (1996b) model of boundedly rational behavioral rules and rule learning for symmetric normal-form games with unique symmetric Nash equilibria. A player begins with initial propensities on a class of evidence-based behavioral rules, and given experience over time adjusts his/her propensities in proportion to the past performance of the rules. An experiment consisting of two 15 period runs with 5x5 games was designed to test this model. The experimental data provide significant support for rule learning and heterogeneity among individuals. We also strongly reject "Nash learning" and "Cournot dynamics" in favor of rule learning.

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Bibliographic Info

Paper provided by The University of Texas at Austin, Center for Applied Research in Economics in its series CARE Working Papers with number 9710.

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Length: 39 pages
Date of creation: Jun 1997
Date of revision:
Handle: RePEc:tex:carewp:9710

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Postal: Austin, Texas 78712
Phone: +1 (512) 471-3211
Fax: +1 (512) 471-3510
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Web page: http://www.utexas.edu/cola/depts/economics/
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References

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  1. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
  2. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  3. Rapoport, Amnon & Erev, Ido & Abraham, Elizabeth V. & Olson, David E., 1997. "Randomization and Adaptive Learning in a Simplified Poker Game," Organizational Behavior and Human Decision Processes, Elsevier, vol. 69(1), pages 31-49, January.
  4. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 925, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  6. Van Huyck, John B & Cook, Joseph P & Battalio, Raymond C, 1994. "Selection Dynamics, Asymptotic Stability, and Adaptive Behavior," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 975-1005, October.
  7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  8. Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
  9. Stahl, D., 1991. "Evolution of Smart-n Players," Discussion Paper 1991-66, Tilburg University, Center for Economic Research.
  10. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  11. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June.
  12. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April.
  13. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
  14. Barry Sopher & Dilip Mookherjee, 1997. "Learning and Decision Costs in Experimental Constant Sum Games," Departmental Working Papers 199527, Rutgers University, Department of Economics.
  15. Dale O. Stahl, 1999. "Evidence based rules and learning in symmetric normal-form games," International Journal of Game Theory, Springer, vol. 28(1), pages 111-130.
  16. 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.
  17. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
  18. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
  19. Mookherjee Dilip & Sopher Barry, 1994. "Learning Behavior in an Experimental Matching Pennies Game," Games and Economic Behavior, Elsevier, vol. 7(1), pages 62-91, July.
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Citations

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Cited by:
  1. Mohlin, Erik, 2010. "Evolution of Theories of Mind," Working Paper Series in Economics and Finance 0728, Stockholm School of Economics, revised 12 May 2010.
  2. Octavian Carare & Ernan Haruvy & Ashutosh Prasad, 2007. "Hierarchical thinking and learning in rank order contests," Experimental Economics, Springer, vol. 10(3), pages 305-316, September.
  3. Camerer, Colin F. & Ho, Teck-Hua & Chong, Juin-Kuan, 2002. "Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games," Journal of Economic Theory, Elsevier, vol. 104(1), pages 137-188, May.
  4. Hanaki, Nobuyuki & Sethi, Rajiv & Erev, Ido & Peterhansl, Alexander, 2005. "Learning strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 523-542, April.
  5. Rapoport, Amnon & Seale, Darryl A. & Winter, Eyal, 2002. "Coordination and Learning Behavior in Large Groups with Asymmetric Players," Games and Economic Behavior, Elsevier, vol. 39(1), pages 111-136, April.
  6. Rick, Scott & Weber, Roberto A., 2010. "Meaningful learning and transfer of learning in games played repeatedly without feedback," Games and Economic Behavior, Elsevier, vol. 68(2), pages 716-730, March.
  7. Chen, Shu-Heng, 2012. "Varieties of agents in agent-based computational economics: A historical and an interdisciplinary perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 1-25.
  8. Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, vol. 62(4), pages 311-333, May.
  9. Shachat, Jason & Walker, Mark, 2004. "Unobserved heterogeneity and equilibrium: an experimental study of Bayesian and adaptive learning in normal form games," Journal of Economic Theory, Elsevier, vol. 114(2), pages 280-309, February.
  10. Stahl, Dale O. & Haruvy, Ernan, 2008. "Level-n bounded rationality in two-player two-stage games," Journal of Economic Behavior & Organization, Elsevier, vol. 65(1), pages 41-61, January.
  11. Rapoport, Amnon & Stein, William E. & Parco, James E. & Nicholas, Thomas E., 2003. "Equilibrium play and adaptive learning in a three-person centipede game," Games and Economic Behavior, Elsevier, vol. 43(2), pages 239-265, May.
  12. Olivier Armantier, 2001. "Does Observation Influence Learning?," Department of Economics Working Papers 01-04, Stony Brook University, Department of Economics.
  13. Haruvy, Ernan & Stahl, Dale O., 2012. "Between-game rule learning in dissimilar symmetric normal-form games," Games and Economic Behavior, Elsevier, vol. 74(1), pages 208-221.
  14. Robert Slonim, 2005. "Competing Against Experienced and Inexperienced Players," Experimental Economics, Springer, vol. 8(1), pages 55-75, April.
  15. Stahl, Dale O., 2001. "Population rule learning in symmetric normal-form games: theory and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 45(1), pages 19-35, May.
  16. Ernan Haruvy & Dale Stahl, 2004. "Level-n Bounded Rationality on a Level Playing Field of Sequential Games," Econometric Society 2004 North American Winter Meetings 126, Econometric Society.
  17. Asim Ansari & Ricardo Montoya & Oded Netzer, 2012. "Dynamic learning in behavioral games: A hidden Markov mixture of experts approach," Quantitative Marketing and Economics, Springer, vol. 10(4), pages 475-503, December.
  18. Haruvy, Ernan & Stahl, Dale O., 2004. "Deductive versus inductive equilibrium selection: experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 53(3), pages 319-331, March.
  19. Mariano Runco, 2013. "Estimating depth of reasoning in a repeated guessing game with no feedback," Experimental Economics, Springer, vol. 16(3), pages 402-413, September.

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