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An equilibrium analysis of the Arad-Rubinstein game

Author

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  • Ewerhart, Christian
  • Kaźmierowski, Stanisław

Abstract

Colonel Blotto games with discrete strategy spaces nicely illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the tie-breaking rule is allowed to be flexible. We begin by pointing out that equilibrium constructions known from the literature extend to our class of games. However, we also note that, irrespective of the tie-breaking rule, the equilibrium set is excessively large. Specifically, any pure strategy that allocates at most twice the fair share to each battlefield is used with positive probability in some equilibrium. Furthermore, refinements based on the elimination of weakly dominated strategies prove ineffective.

Suggested Citation

  • Ewerhart, Christian & Kaźmierowski, Stanisław, 2024. "An equilibrium analysis of the Arad-Rubinstein game," Journal of Economic Behavior & Organization, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:jeborg:v:226:y:2024:i:c:s0167268124003020
    DOI: 10.1016/j.jebo.2024.106696
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    More about this item

    Keywords

    Colonel Blotto games; Multidimensional strategic reasoning; Tie-breaking rules; Nash equilibrium; Dominated strategies;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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