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Bounded Rationality in Randomization

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  • Scroggin, Steven
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    Abstract

    In repeated games with Nash equilibria in mixed strategies, players optimize by playing randomly. Players are boundedly rational in their randomization e�orts. 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 pattern—balance then runs—in 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 sophistication—including a model of the opponent as boundedly rational.

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    Bibliographic Info

    Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt1974b8tz.

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    Date of creation: 01 Sep 2003
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    Handle: RePEc:cdl:ucsdec:qt1974b8tz

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    Keywords: bounded rationality; behavorial game theory;

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    1. 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.
    2. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November.
    3. Rabin, Matthew, 2000. "Inference by Believers in the Law of Small Numbers," Department of Economics, Working Paper Series qt4sw8n41t, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    4. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
    5. 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.
    6. O'Neill, Barry, 1991. "Comments on Brown and Rosenthal's Reexamination [Testing the Minimax Hypothesis, A Reexamination of O'Neill's Game Experiment]," Econometrica, Econometric Society, vol. 59(2), pages 503-07, March.
    7. Shachat, Jason M., 2002. "Mixed Strategy Play and the Minimax Hypothesis," Journal of Economic Theory, Elsevier, vol. 104(1), pages 189-226, May.
    8. 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.
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