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Cognitive ability and learning to play equilibrium: A level-k analysis

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  • David Gill
  • Victoria Prowse

Abstract

In this paper we investigate how cognitive ability influences behavior, success and theevolution of play towards Nash equilibrium in repeated strategic interactions. We study behaviorin a p-beauty contest experiment and find striking differences according to cognitiveability: more cognitively able subjects choose numbers closer to equilibrium, converge morefrequently to equilibrium play and earn more even as behavior approaches the equilibriumprediction. To understand better how subjects with different cognitive abilities learn differently,we estimate a structural model of learning based on level-k reasoning. We find asystematic positive relationship between cognitive ability and levels; furthermore, the averagelevel of more cognitively able subjects responds positively to the cognitive ability of theiropponents, while the average level of less cognitively able subjects does not respond at all.Our results suggest that, in strategic environments, higher cognitive ability translates intobetter analytic reasoning and a better ‘theory of mind

Suggested Citation

  • David Gill & Victoria Prowse, 2013. "Cognitive ability and learning to play equilibrium: A level-k analysis," Economics Series Working Papers 641, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:641
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    2. Geng, Sen & Peng, Yujia & Shachat, Jason & Zhong, Huizhen, 2015. "Adolescents, cognitive ability, and minimax play," Economics Letters, Elsevier, vol. 128(C), pages 54-58.
    3. Camerer, Colin F. & Ho, Teck-Hua, 2015. "Behavioral Game Theory Experiments and Modeling," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Jones, Matthew T., 2014. "Strategic complexity and cooperation: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 352-366.
    5. Carpenter, Jeffrey & Graham, Michael & Wolf, Jesse, 2013. "Cognitive ability and strategic sophistication," Games and Economic Behavior, Elsevier, vol. 80(C), pages 115-130.
    6. Al-Ubaydli, Omar & Jones, Garett & Weel, Jaap, 2016. "Average player traits as predictors of cooperation in a repeated prisoner's dilemma," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 50-60.
    7. Nobuyuki Hanaki & Nicolas Jacquemet & Stéphane Luchini & Adam Zylbersztejn, 2016. "Cognitive ability and the effect of strategic uncertainty," Theory and Decision, Springer, vol. 81(1), pages 101-121, June.
    8. Sheremeta, Roman, 2016. "Impulsive Behavior in Competition: Testing Theories of Overbidding in Rent-Seeking Contests," MPRA Paper 73731, University Library of Munich, Germany.
    9. Georganas, Sotiris & Healy, Paul J. & Weber, Roberto A., 2015. "On the persistence of strategic sophistication," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 369-400.
    10. Maria Cubel & Santiago Sanchez-Pages, 2016. "Gender differences and stereotypes in strategic thinking," UB School of Economics Working Papers 2016/338, University of Barcelona School of Economics.
    11. Heller, Yuval, 2015. "Three steps ahead," Theoretical Economics, Econometric Society, vol. 10(1), January.
    12. Mikhail Drugov & Roberto Hernán-González & Praveen Kujal & Marta Troya Martinez, 2013. "Cheap Talk with Two Audiences: An Experiment," Working Papers 13-32, Chapman University, Economic Science Institute.
    13. Shu-Heng Chen & Ye-Rong Du & Lee-Xieng Yang, 2014. "Cognitive capacity and cognitive hierarchy: a study based on beauty contest experiments," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 9(1), pages 69-105, April.
    14. Dietmar Fehr & Steffen Huck, 2016. "Who knows it is a game? On strategic awareness and cognitive ability," Experimental Economics, Springer;Economic Science Association, vol. 19(4), pages 713-726, December.
    15. Brañas-Garza, Pablo & García-Muñoz, Teresa & González, Roberto Hernán, 2012. "Cognitive effort in the Beauty Contest Game," Journal of Economic Behavior & Organization, Elsevier, vol. 83(2), pages 254-260.
    16. Allred, Sarah & Duffy, Sean & Smith, John, 2016. "Cognitive load and strategic sophistication," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 162-178.
    17. Bayer, Ralph C. & Renou, Ludovic, 2016. "Logical omniscience at the laboratory," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 41-49.
    18. Duffy, Sean & Smith, John, 2014. "Cognitive load in the multi-player prisoner's dilemma game: Are there brains in games?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 51(C), pages 47-56.
    19. Adam Sanjurjo, 2015. "Search, Memory, and Choice Error: An Experiment," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-16, June.
    20. Baghestanian, Sascha & Frey, Seth, 2016. "GO figure: Analytic and strategic skills are separable," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 71-80.
    21. Chen, Chia-Ching & Chiu, I-Ming & Smith, John & Yamada, Tetsuji, 2013. "Too smart to be selfish? Measures of cognitive ability, social preferences, and consistency," Journal of Economic Behavior & Organization, Elsevier, vol. 90(C), pages 112-122.
    22. Fehr, Dietmar & Huck, Steffen, 2013. "Who knows It is a game? On rule understanding, strategic awareness and cognitive ability," Discussion Papers, Research Unit: Economics of Change SP II 2013-306, WZB Berlin Social Science Center.

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    More about this item

    Keywords

    Cognitive ability; bounded rationality; level-k; convergence; learning non-equilibrium behavior; beauty contest; repeated games; structural modeling; theory of mind; intelligence; Raven test;
    All these keywords.

    JEL classification:

    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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