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Endogenous Depth of Reasoning

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  • Larbi Alaoui
  • Antonio Penta

Abstract

We introduce a model of strategic thinking in games of initial response. Unlike standard level-k models, 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. Our approach therefore serves as a novel, unifying framework of strategic thinking in games.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 653.

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Date of creation: Mar 2014
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Handle: RePEc:bge:wpaper:653

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

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References

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  1. Grosskopf, Brit & Nagel, Rosemarie, 2008. "The two-person beauty contest," Games and Economic Behavior, Elsevier, vol. 62(1), pages 93-99, January.
  2. Tomasz Strzalecki, 1969. "Depth of Reasoning and Higher Order Beliefs," Working Paper 8334, Harvard University OpenScholar.
  3. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
  4. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
  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. 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. Choo, Lawrence C.Y & Kaplan, Todd R., 2014. "Explaining Behavior in the "11-20" Game," MPRA Paper 52808, University Library of Munich, Germany.
  2. María Cubel & Santiago Sanchez-Pages, 2014. "Gender differences and stereotypes in the beauty contest," Working Papers 2014/13, Institut d'Economia de Barcelona (IEB).
  3. Allred, Sarah & Duffy, Sean & Smith, John, 2013. "Cognitive Load and Strategic Sophistication," MPRA Paper 47997, University Library of Munich, Germany.

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