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Endogenous depth of reasoning

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Abstract

We introduce a model of strategic thinking in games of initial response. Unlike standard models of strategic thinking, in this framework the player's "depth of reasoning" is endogenously determined, and it can be disentangled from his beliefs over his opponent's cognitive bound. In our approach, individuals act as if they follow a cost-benefit analysis. The depth of reasoning is a function of the player's cognitive abilities and his payoffs. The costs are exogenous and represent the game theoretical sophistication of the player; the benefit instead is related to the game payoffs. Behavior is in turn determined by the individual's depth of reasoning and his beliefs about the reasoning process of the opponent. Thus, in our framework, payoffs not only affect individual choices in the traditional sense, but they also shape the cognitive process itself. Our model delivers testable implications on players' chosen actions as incentives and opponents change. We then test the model's predictions with an experiment. We administer different treatments that vary beliefs over payoffs and opponents, as well as beliefs over opponents' beliefs. The results of this experiment, which are not accounted for by current models of reasoning in games, strongly support our theory. We also show that the predictions of our model are highly consistent quantitatively with well-known unresolved empirical puzzles. Our approach therefore serves as a novel, unifying framework of strategic thinking that allows for predictions across games.

Suggested Citation

  • Larbi Alaoui & Antonio Penta, 2012. "Endogenous depth of reasoning," Economics Working Papers 1332, Department of Economics and Business, Universitat Pompeu Fabra, revised Mar 2014.
  • Handle: RePEc:upf:upfgen:1332
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    References listed on IDEAS

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    1. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
    2. 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.
    3. 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.
    4. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    5. 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.
    6. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
    7. Grosskopf, Brit & Nagel, Rosemarie, 2008. "The two-person beauty contest," Games and Economic Behavior, Elsevier, vol. 62(1), pages 93-99, January.
    8. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
    9. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:

    1. Wagner, Alexander K. & Granic, Dura-Georg, 2017. "Tie-Breaking Power in Committees," Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168187, Verein für Socialpolitik / German Economic Association.
    2. Marco Mantovani, 2015. "Limited backward induction: foresight and behavior in sequential games," Working Papers 289, University of Milano-Bicocca, Department of Economics, revised Jan 2015.
    3. Marianna Belloc & Ennio Bilancini & Leonardo Boncinelli & Simone D'Alessandro, 2017. "A Social Heuristics Hypothesis for the Stag Hunt: Fast- and Slow-Thinking Hunters in the Lab," CESifo Working Paper Series 6824, CESifo Group Munich.
    4. repec:eee:gamebe:v:107:y:2018:i:c:p:153-181 is not listed on IDEAS
    5. Külpmann, Philipp & Khantadze, Davit, 2016. "Identifying the reasons for coordination failure in a laboratory experiment," Center for Mathematical Economics Working Papers 567, Center for Mathematical Economics, Bielefeld University.
    6. repec:eee:matsoc:v:90:y:2017:i:c:p:191-207 is not listed on IDEAS
    7. Yukio Koriyama & Ali Ozkes, 2017. "Condorcet Jury Theorem and Cognitive Hierarchies: Theory and Experiments," Working Papers halshs-01485748, HAL.
    8. Larbi Alaoui & Antonio Penta, 2017. "Reasoning about Others’ Reasoning," Working Papers 1003, Barcelona Graduate School of Economics.
    9. Matthew Embrey & Guillaume R. Frechette & Sevgi Yuksel, 2016. "Cooperation in the Finitely Repeated Prisoner's Dilemma," Working Paper Series 08616, Department of Economics, University of Sussex.
    10. Allred, Sarah & Duffy, Sean & Smith, John, 2016. "Cognitive load and strategic sophistication," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 162-178.
    11. Nagel, Rosemarie & Bühren, Christoph & Frank, Björn, 2017. "Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 191-207.
    12. Larbi Alaoui & Antonio Penta, 2017. "Reasoning about others’ reasoning," Economics Working Papers 1587, Department of Economics and Business, Universitat Pompeu Fabra.
    13. Ennio Bilancini & Leonardo Boncinelli, 2014. "Persuasion with Reference Cues and Elaboration Costs," Center for Economic Research (RECent) 102, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    14. Maria Cubel & Santiago Sanchez-Pages, 2016. "Gender differences and stereotypes in strategic thinking," UB Economics Working Papers 2016/338, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.
    15. Choo, Lawrence C.Y & Kaplan, Todd R., 2014. "Explaining Behavior in the "11-20" Game," MPRA Paper 52808, University Library of Munich, Germany.
    16. 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.
    17. Sandomirskaia, Marina, 2017. "Nash-2 equilibrium: selective farsightedness under uncertain response," MPRA Paper 83152, University Library of Munich, Germany.
    18. Eugenio Proto & Aldo Rustichini & Andis Sofianos, 2016. "Intelligence, Personality and Gains from Cooperation in Repeated Interactions," CESifo Working Paper Series 6121, CESifo Group Munich.
    19. María Cubel & Santiago Sanchez-Pages, 2014. "Gender differences and stereotypes in the beauty contest," Working Papers 2014/13, Institut d'Economia de Barcelona (IEB).

    More about this item

    Keywords

    cognitive cost ; depth of reasoning; higher order beliefs; level-k reasoning; strategic thinking;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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