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Multi-Dimensional Iterative Reasoning in Action: The Case of the Colonel Blotto Game

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  • Ayala Arad
  • Ariel Rubinstein

Abstract

We introduce a novel decision procedure involving multi-dimensional iterative reasoning, in which a player decides separately on the various features of his strategy using an iterative process. This type of strategic reasoning fits a range of complicated situations in which a player faces a large and non-ordered strategy space. In this paper, the procedure is used to explain the results of a large web-based experiment of a tournament version of the Colonel Blotto game. The interpretation of the participants’ choices as reflecting multi-dimensional iterative reasoning is supported by an analysis of their response times and the relation between the participants’ behavior in this game and their choices in another game which triggers standard k-level reasoning. Finally, we reveal the most successful strategies in the tournament, which appear to reflect 2–3 levels of reasoning in the two main “dimensions”.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000497.

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Date of creation: 11 Sep 2012
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Handle: RePEc:cla:levarc:786969000000000497

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  1. Ayala Arad & Ariel Rubinstein, 2013. "Strategic Tournaments," American Economic Journal: Microeconomics, American Economic Association, vol. 5(4), pages 31-54, November.
  2. Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Levine's Bibliography 321307000000000532, UCLA Department of Economics.
  3. Ariel Rubinstein, 2006. "Instinctive and Cognitive Reasoning: A Study of Response Times," Working Papers 2006.36, Fondazione Eni Enrico Mattei.
  4. Subhasish Chowdhury & Dan Kovenock & Roman Sheremeta, 2013. "An experimental investigation of Colonel Blotto games," Economic Theory, Springer, vol. 52(3), pages 833-861, April.
  5. Ayala Arad & Ariel Rubinstein, 2012. "The 11-20 Money Request Game: A Level-k Reasoning Study," American Economic Review, American Economic Association, vol. 102(7), pages 3561-73, December.
  6. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  7. Hortala-Vallve, Rafael & Llorente-Saguer, Aniol, 2010. "A simple mechanism for resolving conflict," Games and Economic Behavior, Elsevier, vol. 70(2), pages 375-391, November.
  8. Yetkin ÇINAR & Türkmen GÖKSEL, 2012. "An experimental analysis of Colonel Blotto Games under alternative environments," Iktisat Isletme ve Finans, Bilgesel Yayincilik, vol. 27(312), pages 39-57.
  9. 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.
  10. 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.
  11. Arad Ayala, 2012. "The Tennis Coach Problem: A Game-Theoretic and Experimental Study," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-43, April.
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Cited by:
  1. Montero García, Maria & Possajennikow, Alex & Sefton, Martín & Turocy, Theodore L., 2013. "Majoritarian Contests with Asymmetric Battlefields: An Experiment," IKERLANAK Ikerlanak;2013-76, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  2. Lindner, Florian & Sutter, Matthias, 2013. "Level-k reasoning and time pressure in the 11–20 money request game," Economics Letters, Elsevier, vol. 120(3), pages 542-545.
  3. John Duffy & Alexander Matros, 2013. "Stochastic Asymmetric Blotto Games: Theory and Experimental Evidence," Working Papers 509, University of Pittsburgh, Department of Economics, revised Nov 2013.
  4. Ariel Rubenstein, 2013. "Response time and decision making: An experimental study," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 8(5), pages 540-551, September.
  5. R. M. Harstad & R. Selten., 2014. "Bounded-Rationality Models: Tasks to Become Intellectually Competitive," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 5.
  6. Vincent P. Crawford, 2013. "Boundedly Rational versus Optimization-Based Models of Strategic Thinking and Learning in Games," Journal of Economic Literature, American Economic Association, vol. 51(2), pages 512-27, June.
  7. Ralf Bergheim & Michael W.M. Roos, 2013. "Intuition and Reasoning in Choosing Ambiguous and Risky Lotteries," Ruhr Economic Papers 0440, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.

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