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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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  • Ayala Arad & Ariel Rubinstein, 2012. "Multi-Dimensional Iterative Reasoning in Action: The Case of the Colonel Blotto Game," Levine's Working Paper Archive 786969000000000497, David K. Levine.
    • Handle: RePEc:cla:levarc:786969000000000497
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    References listed on IDEAS

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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

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