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An equilibrium analysis of the Arad-Rubinstein game

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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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    References listed on IDEAS

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    1. Dechenaux, Emmanuel & Kovenock, Dan & Lugovskyy, Volodymyr, 2006. "Caps on bidding in all-pay auctions: Comments on the experiments of A. Rapoport and W. Amaldoss," Journal of Economic Behavior & Organization, Elsevier, vol. 61(2), pages 276-283, October.
    2. Subhasish Chowdhury & Dan Kovenock & Roman Sheremeta, 2013. "An experimental investigation of Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 833-861, April.
    3. Ayala Arad & Ariel Rubinstein, 2019. "Multidimensional Reasoning in Games: Framework, Equilibrium, and Applications," American Economic Journal: Microeconomics, American Economic Association, vol. 11(3), pages 285-318, August.
    4. Avrahami, Judith & Kareev, Yaakov & Todd, Peter M. & Silverman, Boaz, 2014. "Allocation of resources in asymmetric competitions: How do the weak maintain a chance of winning?," Journal of Economic Psychology, Elsevier, vol. 42(C), pages 161-174.
    5. Maria Montero & Alex Possajennikov & Martin Sefton & Theodore Turocy, 2016. "Majoritarian Blotto contests with asymmetric battlefields: an experiment on apex games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 55-89, January.
    6. Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 441-460, March.
    7. Arad, Ayala & Rubinstein, Ariel, 2012. "Multi-dimensional iterative reasoning in action: The case of the Colonel Blotto game," Journal of Economic Behavior & Organization, Elsevier, vol. 84(2), pages 571-585.
    8. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    9. Christian Ewerhart & Stanisław Kaźmierowski, 2024. "An equilibrium analysis of the Arad-Rubinstein game," ECON - Working Papers 443, Department of Economics - University of Zurich.
    10. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 1-24, September.
    11. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    12. Ewerhart, Christian & Kaźmierowski, Stanisław, 2024. "An equilibrium analysis of the Arad-Rubinstein game," Journal of Economic Behavior & Organization, Elsevier, vol. 226(C).
    13. Rapoport, Amnon & Amaldoss, Wilfred, 2000. "Mixed strategies and iterative elimination of strongly dominated strategies: an experimental investigation of states of knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 42(4), pages 483-521, August.
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    1. Ewerhart, Christian & Kaźmierowski, Stanisław, 2024. "An equilibrium analysis of the Arad-Rubinstein game," Journal of Economic Behavior & Organization, Elsevier, vol. 226(C).

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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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