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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, 2012. "Strategic Tournaments," Levine's Bibliography 786969000000000438, UCLA Department of Economics.
  2. Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer, vol. 36(3), pages 441-460, March.
  3. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  4. Chowdhury, Subhasish & Kovenock, Dan & Sheremeta, Roman, 2011. "An Experimental Investigation of Colonel Blotto Games," MPRA Paper 46810, University Library of Munich, Germany.
  5. 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.
  6. Vincent P. Crawford & Nagore Iriberri, 2007. "Fatal Attraction: Salience, Naivete, and Sophistication in Experimental Hide-and-Seek Games," Levine's Bibliography 321307000000000861, UCLA Department of Economics.
  7. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: A Study of Response Times," Economic Journal, Royal Economic Society, vol. 117(523), pages 1243-1259, October.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
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Cited by:
  1. V. P. Crawford., 2014. "Boundedly Rational versus Optimization-Based Models of Strategic Thinking and Learning in Games," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 5.
  2. Lindner, Florian & Sutter, Matthias, 2013. "Level-k reasoning and time pressure in the 11-20 money request game," Munich Reprints in Economics 19234, University of Munich, Department of Economics.
  3. 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.
  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. 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.
  6. Maria Montero & Alex Possajennikov & Martin Sefton & Theodore Turocy, 2013. "Majoritarian Contests with Asymmetric Battlefields: An Experiment," Discussion Papers 2013-12, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  7. R. M. Harstad & R. Selten., 2014. "Bounded-Rationality Models: Tasks to Become Intellectually Competitive," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 5.

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