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

  • Ayala Arad
  • Ariel Rubinstein

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
Contact details of provider: Web page: http://www.dklevine.com/

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  1. Ayala Arad & Ariel Rubinstein, 2012. "Strategic Tournaments," Levine's Bibliography 786969000000000438, UCLA Department of Economics.
  2. Subhasish M. Chowdhury & Dan Kovenock J. & Roman M. Sheremeta, 2009. "An Experimental Investigation of Colonel Blotto Games," CESifo Working Paper Series 2688, CESifo Group Munich.
  3. 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.
  4. Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer, vol. 36(3), pages 441-460, March.
  5. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: A Study of Response Times," Economic Journal, Royal Economic Society, vol. 117(523), pages 1243-1259, October.
  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. 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.
  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. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  10. 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.
  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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