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Endogenous Depth of Reasoning

  • Larbi Alaoui
  • Antonio Penta

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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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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  1. Miguel A. Costa-Gomes & Vincent P. Crawford, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," Levine's Bibliography 321307000000000336, UCLA Department of Economics.
  2. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
  3. 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.
  4. Davidson, R. & Duclos, J.-Y., 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," G.R.E.Q.A.M. 98a14, Universite Aix-Marseille III.
  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. Tomasz Strzalecki, . "Depth of Reasoning and Higher Order Beliefs," Working Paper 8334, Harvard University OpenScholar.
  7. C. Monica Capra, 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June.
  8. Grosskopf, Brit & Nagel, Rosemarie, 2008. "The two-person beauty contest," Games and Economic Behavior, Elsevier, vol. 62(1), pages 93-99, January.
  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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