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

Author

Listed:
  • 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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    1. Thomas Dohmen & Armin Falk & David Huffman & Uwe Sunde, 2010. "Are Risk Aversion and Impatience Related to Cognitive Ability?," American Economic Review, American Economic Association, vol. 100(3), pages 1238-1260, June.
    2. 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.
    3. 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.
    4. Antoni Bosch-Domènech & José G. Montalvo & Rosemarie Nagel & Albert Satorra, 2002. "One, Two, (Three), Infinity, ...: Newspaper and Lab Beauty-Contest Experiments," American Economic Review, American Economic Association, vol. 92(5), pages 1687-1701, December.
    5. Ohtsubo, Yohsuke & Rapoport, Amnon, 2006. "Depth of reasoning in strategic form games," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 35(1), pages 31-47, February.
    6. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
    7. Miguel A. Costa-Gomes & Georg Weizsäcker, 2008. "Stated Beliefs and Play in Normal-Form Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 729-762.
    8. Rydval, Ondrej & Ortmann, Andreas & Ostatnicky, Michal, 2009. "Three very simple games and what it takes to solve them," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 589-601, October.
    9. Yan Chen & Robert Gazzale, 2004. "When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting," American Economic Review, American Economic Association, vol. 94(5), pages 1505-1535, December.
    10. Duffy, John & Nagel, Rosemarie, 1997. "On the Robustness of Behaviour in Experimental "Beauty Contest" Games," Economic Journal, Royal Economic Society, vol. 107(445), pages 1684-1700, November.
    11. Brañas-Garza, Pablo & Espinosa, María Paz & Rey-Biel, Pedro, 2011. "Travelers' types," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 25-36, April.
    12. 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.
    13. James J. Heckman & Jora Stixrud & Sergio Urzua, 2006. "The Effects of Cognitive and Noncognitive Abilities on Labor Market Outcomes and Social Behavior," Journal of Labor Economics, University of Chicago Press, vol. 24(3), pages 411-482, July.
    14. Dessi, Roberta & Rustichini, Aldo, 2011. "Work for Image and Work for Pay," TSE Working Papers 11-252, Toulouse School of Economics (TSE).
    15. Ignacio Palacios-Huerta & Oscar Volij, 2009. "Field Centipedes," American Economic Review, American Economic Association, vol. 99(4), pages 1619-1635, September.
    16. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    17. Stahl, Dale O., 1996. "Boundedly Rational Rule Learning in a Guessing Game," Games and Economic Behavior, Elsevier, vol. 16(2), pages 303-330, October.
    18. Ho, Teck-Hua & Camerer, Colin & Weigelt, Keith, 1998. "Iterated Dominance and Iterated Best Response in Experimental "p-Beauty Contests."," American Economic Review, American Economic Association, vol. 88(4), pages 947-969, September.
    19. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    20. Oechssler, Jörg & Roider, Andreas & Schmitz, Patrick W., 2009. "Cognitive abilities and behavioral biases," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 147-152, October.
    21. Vincent P. Crawford & Nagore Iriberri, 2007. "Level-k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?," Econometrica, Econometric Society, vol. 75(6), pages 1721-1770, November.
    22. Burnham, Terence C. & Cesarini, David & Johannesson, Magnus & Lichtenstein, Paul & Wallace, Björn, 2009. "Higher cognitive ability is associated with lower entries in a p-beauty contest," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 171-175, October.
    23. Agranov, Marina & Potamites, Elizabeth & Schotter, Andrew & Tergiman, Chloe, 2012. "Beliefs and endogenous cognitive levels: An experimental study," Games and Economic Behavior, Elsevier, vol. 75(2), pages 449-463.
    24. Dufwenberg, Martin & Sundaram, Ramya & Butler, David J., 2010. "Epiphany in the Game of 21," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 132-143, August.
    25. Bergman, Oscar & Ellingsen, Tore & Johannesson, Magnus & Svensson, Cicek, 2010. "Anchoring and cognitive ability," Economics Letters, Elsevier, vol. 107(1), pages 66-68, April.
    26. Avi Goldfarb & Mo Xiao, 2011. "Who Thinks about the Competition? Managerial Ability and Strategic Entry in US Local Telephone Markets," American Economic Review, American Economic Association, vol. 101(7), pages 3130-3161, December.
    27. Robert Östling & Joseph Tao-yi Wang & Eileen Y. Chou & Colin F. Camerer, 2011. "Testing Game Theory in the Field: Swedish LUPI Lottery Games," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 1-33, August.
    28. Broseta, Bruno & Costa-Gomes, Miguel & Crawford, Vincent P., 2000. "Cognition and Behavior in Normal-Form Games: An Experimental Study," University of California at San Diego, Economics Working Paper Series qt0fp8278k, Department of Economics, UC San Diego.
    29. Theo Offerman & Jan Potters & Joep Sonnemans, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(4), pages 973-997.
    30. Lex Borghans & Bart H. H. Golsteyn & James J. Heckman & Huub Meijers, 2009. "Gender Differences in Risk Aversion and Ambiguity Aversion," Journal of the European Economic Association, MIT Press, vol. 7(2-3), pages 649-658, 04-05.
    31. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
    32. Burks, Stephen V. & Carpenter, Jeffrey P. & Götte, Lorenz & Rustichini, Aldo, 2008. "Cognitive Skills Explain Economic Preferences, Strategic Behavior, and Job Attachment," IZA Discussion Papers 3609, Institute of Labor Economics (IZA).
    33. 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.
    34. Ralph-C. Bayer & Ludovic Renou, 2011. "Cognitive abilities and behavior in strategic-form games.," Discussion Papers in Economics 11/16, Division of Economics, School of Business, University of Leicester.
    35. Vincent P. Crawford & Nagore Iriberri, 2007. "Fatal Attraction: Salience, Naïveté, and Sophistication in Experimental "Hide-and-Seek" Games," American Economic Review, American Economic Association, vol. 97(5), pages 1731-1750, December.
    36. Oliver Schnusenberg & Andrés Gallo, 2011. "On Cognitive Ability and Learning in a Beauty Contest," Journal for Economic Educators, Middle Tennessee State University, Business and Economic Research Center, vol. 11(1), pages 13-24, Summer.
    37. Al-Ubaydli, Omar & Jones, Garett & Weel, Jaap, 2010. "Patience, cognitive skill and coordination in the repeated stag hunt," MPRA Paper 27723, University Library of Munich, Germany.
    38. Gary Charness & Aldo Rustichini & Jeroen van de Ven, 2011. "Self-Confidence and Strategic Deterrence," Tinbergen Institute Discussion Papers 11-151/1, Tinbergen Institute.
    39. repec:mpr:mprres:7497 is not listed on IDEAS
    40. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September.
    41. Shane Frederick, 2005. "Cognitive Reflection and Decision Making," Journal of Economic Perspectives, American Economic Association, vol. 19(4), pages 25-42, Fall.
    42. Daniel J. Benjamin & Sebastian A. Brown & Jesse M. Shapiro, 2013. "Who Is ‘Behavioral’? Cognitive Ability And Anomalous Preferences," Journal of the European Economic Association, European Economic Association, vol. 11(6), pages 1231-1255, December.
    43. Lex Borghans & Bart H.H. Golsteyn & James J. Heckman & Huub Meijers, 2009. "Gender Differences in Risk Aversion and Ambiguity," Working Papers 200903, Geary Institute, University College Dublin.
    44. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
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    Cited by:

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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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