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Waging simple wars: a complete characterization of two-battlefield Blotto equilibria

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We analyze the strategic allocation of resources across two contests as in the canonical Colonel Blotto game. In the games we study, two players simultaneously allocate their forces across two fields of battle. The larger force on each battlefield wins that battle, and the payoff to a player is the sum of the values of battlefields won. We completely characterize the set of Nash equilibria of all two-battlefield Blotto games and provide the unique equilibrium payoffs. We also show how to extend our characterization to cover previously unstudied games with nonlinear resource constraints. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • 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.
    • Handle: RePEc:spr:joecth:v:58:y:2015:i:1:p:183-216
    DOI: 10.1007/s00199-014-0807-1
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    Cited by:

    1. Subhasish M Chowdhury & Dan Kovenock & David Rojo Arjona & Nathaniel T Wilcox, 2021. "Focality and Asymmetry in Multi-Battle Contests," The Economic Journal, Royal Economic Society, vol. 131(636), pages 1593-1619.
    2. Dan Kovenock & Brian Roberson & Roman M. Sheremeta, 2019. "The attack and defense of weakest-link networks," Public Choice, Springer, vol. 179(3), pages 175-194, June.
    3. Li, Xinmi & Zheng, Jie, 2022. "Pure strategy Nash Equilibrium in 2-contestant generalized lottery Colonel Blotto games," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    4. Raphael Boleslavsky & Christopher Cotton, 2018. "Limited capacity in project selection: competition through evidence production," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 385-421, March.
    5. Dan Kovenock & Brian Roberson, 2015. "The Optimal Defense of Network Connectivity," Working Papers 15-24, Chapman University, Economic Science Institute.
    6. 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.
    7. Dan Kovenock & Brian Roberson, 2018. "The Optimal Defense Of Networks Of Targets," Economic Inquiry, Western Economic Association International, vol. 56(4), pages 2195-2211, October.
    8. Dmitry Dagaev & Andrey Zubanov, 2022. "Round-robin tournaments with limited resources," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 525-583, October.
    9. Cortes-Corrales, Sebastián & Gorny, Paul M., 2018. "Generalising Conflict Networks," MPRA Paper 90001, University Library of Munich, Germany.
    10. Kostyantyn Mazur, 2017. "A Partial Solution to Continuous Blotto," Papers 1706.08479, arXiv.org, revised Sep 2017.

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    More about this item

    Keywords

    Colonel Blotto game; Zero-sum game; Warfare; All-pay auction; Multi-unit auction; C72; H56; D7;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • H56 - Public Economics - - National Government Expenditures and Related Policies - - - National Security and War
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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