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An equilibrium analysis of the Arad-Rubinstein game


Ewerhart, Christian; Kaźmierowski, Stanisław (2024). An equilibrium analysis of the Arad-Rubinstein game. Working paper series / Department of Economics 443, University of Zurich.

Abstract

Colonel Blotto games with discrete strategy spaces effectively 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. To derive specific predictions amid this multiplicity, we compute strategies resulting from long-run adaptive learning.

Abstract

Colonel Blotto games with discrete strategy spaces effectively 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. To derive specific predictions amid this multiplicity, we compute strategies resulting from long-run adaptive learning.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Economics
Working Paper Series > Department of Economics
Dewey Decimal Classification:330 Economics
JEL Classification:C72, C91, D74
Uncontrolled Keywords:Colonel Blotto games, multidimensional strategic reasoning, tiebreaking rules, Nash equilibrium, dominated strategies, adaptive learning
Scope:Discipline-based scholarship (basic research)
Language:English
Date:March 2024
Deposited On:15 Mar 2024 11:10
Last Modified:15 Mar 2024 21:50
Series Name:Working paper series / Department of Economics
Number of Pages:33
ISSN:1664-7041
OA Status:Green
Related URLs:https://www.econ.uzh.ch/en/research/workingpapers.html
  • Content: Published Version
  • Language: English