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A Partial Solution to Continuous Blotto

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  • Kostyantyn Mazur

Abstract

This paper analyzes the structure of mixed-strategy equilibria for Colonel Blotto games, where the outcome on each battlefield is a polynomial function of the difference between the two players' allocations. This paper severely reduces the set of strategies that needs to be searched to find a Nash equilibrium. It finds that there exists a Nash equilibrium where both players' mixed strategies are discrete distributions, and it places an upper bound on the number of points in the supports of these discrete distributions.

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  • Kostyantyn Mazur, 2017. "A Partial Solution to Continuous Blotto," Papers 1706.08479, arXiv.org, revised Sep 2017.
    • Handle: RePEc:arx:papers:1706.08479
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    References listed on IDEAS

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    1. Weinstein Jonathan, 2012. "Two Notes on the Blotto Game," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-13, March.
    2. Russell Golman & Scott Page, 2009. "General Blotto: games of allocative strategic mismatch," Public Choice, Springer, vol. 138(3), pages 279-299, March.
    3. Dan Kovenock & Brian Roberson, 2021. "Generalizations of the General Lotto and Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 997-1032, April.
    4. Brian Roberson & Dmitriy Kvasov, 2012. "The non-constant-sum Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 397-433, October.
    5. Scott Macdonell & Nick Mastronardi, 2015. "Waging simple wars: a complete characterization of two-battlefield Blotto equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 183-216, 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. Caroline D. Thomas, 2009. "N-Dimensional Blotto Game with Asymmetric Battlefield Values," Department of Economics Working Papers 130116, The University of Texas at Austin, Department of Economics, revised Dec 2016.
    8. Rafael Hortala-Vallve & Aniol Llorente-Saguer, 2012. "Pure strategy Nash equilibria in non-zero sum colonel Blotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 331-343, May.
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