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Bounded Rationality in Randomization

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Author Info
Steven Scroggin (University of California, San Diego)
Abstract

In repeated games with Nash equilibria in mixed strategies, players optimize by playing randomly. Players are boundedly rational in their randomization eorts. Arguably, they have no internal randomization facility and they fashion external randomization aids from the environment. By conditioning on past play, boundedly rational players exhibit a pattern. The pattern is characterized by cognitive limitations variously called local representativeness, the law of small numbers or the gambler's fallacy. I find one such patternbalance then runsin re-analysis of existing data for matching pennies experiments. While players and play are heterogeneous, the pattern makes prediction plausible. I implement prediction with a non-linear autoregression. Model 1 is a statistically and substantively significant tool for predicting behavior in matching pennies. There is evidence for two other behavioral models, both of which require some sort of sophisticationincluding a model of the opponent as boundedly rational.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 2003-13.

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Date of creation: 11 Jul 2004
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Handle: RePEc:cdl:ucsdec:2003-13

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Keywords: bounded rationality; behavorial game theory;

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  1. 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. [Downloadable!] (restricted)
  2. Matthew Rabin, 2002. "Inference By Believers In The Law Of Small Numbers," The Quarterly Journal of Economics, MIT Press, vol. 117(3), pages 775-816, August. [Downloadable!] (restricted)
  3. Oechssler, Jorg & Schipper, Burkhard, 2003. "Can you guess the game you are playing?," Games and Economic Behavior, Elsevier, vol. 43(1), pages 137-152, April. [Downloadable!] (restricted)
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  4. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine. [Downloadable!]
  5. 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. [Downloadable!] (restricted)
  6. Shachat, Jason M., 2002. "Mixed Strategy Play and the Minimax Hypothesis," Journal of Economic Theory, Elsevier, vol. 104(1), pages 189-226, May. [Downloadable!] (restricted)
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  7. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
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  8. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November. [Downloadable!] (restricted)
  9. Brown, James N & Rosenthal, Robert W, 1990. "Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment," Econometrica, Econometric Society, vol. 58(5), pages 1065-81, September. [Downloadable!] (restricted)
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