An equilibrium analysis of the Arad-Rubinstein game

Christian Ewerhart and Stanisław Kaźmierowski

Journal of Economic Behavior & Organization, 2024, vol. 226, issue C

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.

Keywords: Colonel Blotto games; Multidimensional strategic reasoning; Tie-breaking rules; Nash equilibrium; Dominated strategies (search for similar items in EconPapers)
JEL-codes: C72 C91 D74 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jeborg:v:226:y:2024:i:c:s0167268124003020

DOI: 10.1016/j.jebo.2024.106696

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