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Multi-dimensional iterative reasoning in action: The case of the Colonel Blotto game

  • Arad, Ayala
  • Rubinstein, Ariel

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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Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

Volume (Year): 84 (2012)
Issue (Month): 2 ()
Pages: 571-585

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Handle: RePEc:eee:jeborg:v:84:y:2012:i:2:p:571-585
Contact details of provider: Web page: http://www.elsevier.com/locate/jebo

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  1. 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.
  2. Ayala Arad & Ariel Rubinstein, 2013. "Strategic Tournaments," American Economic Journal: Microeconomics, American Economic Association, vol. 5(4), pages 31-54, November.
  3. 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.
  4. Chowdhury, Subhasish M. & Kovenock, Dan & Sheremeta, Roman M., 2009. "An experimental investigation of Colonel Blotto games
    [Eine experimentelle Untersuchung von „Colonel Blotto“-Spielen]
    ," Discussion Papers, Research Unit: Market Processes and Governance SP II 2009-08, Social Science Research Center Berlin (WZB).
  5. 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.
  6. 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.
  7. Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Levine's Bibliography 321307000000000532, UCLA Department of Economics.
  8. Ariel Rubinstein, 2006. "Instinctive and Cognitive Reasoning: A Study of Response Times," Working Papers 2006.36, Fondazione Eni Enrico Mattei.
  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. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  11. 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.
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