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Coalitional Colonel Blotto Games with Application to the Economics of Alliances

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  • Dan Kovenock
  • Brian Roberson

Abstract

This paper examines a multi-player and multi-front Colonel Blotto game in which one player, A, simultaneously competes in two disjoint Colonel Blotto games, against two separate opponents, 1 and 2. Prior to competing in the games, players 1 and 2 have the opportunity to form an alliance to share their endowments of a one-dimensional resource (e.g., troops, military hardware, money). This paper examines “non-cooperative” alliances in which only individually rational ex ante transfers of the resource are allowed. Once these transfers take place, each alliance member maximizes his payoff in his respective Colonel Blotto game, given his resource constraint and player A’s allocation of its endowment across the two games. No ex post transfers are enforceable. Remarkably, there are several ranges of parameters in which endogenous unilateral transfers take place within the alliance. That is, one player gives away resources to his ally, who happily accepts the gift. Unilateral transfers arise because they lead to a strategic shift in the common opponent’s force allocation away from the set of battlefields of the player making the transfer, towards the set of battlefields of the player receiving the transfer. Our result demonstrates that there exist unilateral transfers for which the combination of direct and strategic effects benefits both allies. This stands in stark contrast to the previous literature on alliances (see Sandler and Hartley, 2001), which relies on the assumption of pure or impure public goods.

Suggested Citation

  • Dan Kovenock & Brian Roberson, 2007. "Coalitional Colonel Blotto Games with Application to the Economics of Alliances," Purdue University Economics Working Papers 1207, Purdue University, Department of Economics.
  • Handle: RePEc:pur:prukra:1207
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    References listed on IDEAS

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    1. Todd Sandler, 1999. "Alliance Formation, Alliance Expansion, and the Core," Journal of Conflict Resolution, Peace Science Society (International), vol. 43(6), pages 727-747, December.
    2. Murdoch, James C. & Sandler, Todd, 1984. "Complementarity, free riding, and the military expenditures of NATO allies," Journal of Public Economics, Elsevier, vol. 25(1-2), pages 83-101, November.
    3. Todd Sandler, 1993. "The Economic Theory of Alliances," Journal of Conflict Resolution, Peace Science Society (International), vol. 37(3), pages 446-483, September.
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    6. Keith Hartley & Todd Sandler, 2001. "Economics of Alliances: The Lessons for Collective Action," Journal of Economic Literature, American Economic Association, vol. 39(3), pages 869-896, September.
    7. Skaperdas, Stergios, 1998. "On the Formation of Alliances in Conflict and Contests," Public Choice, Springer, vol. 96(1-2), pages 25-42, July.
    8. 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.
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    Cited by:

    1. Konrad, Kai A. & Kovenock, Dan, 2009. "The alliance formation puzzle and capacity constraints," Economics Letters, Elsevier, vol. 103(2), pages 84-86, May.
    2. Casella, Alessandra & Laslier, Jean-François & Macé, Antonin, 2017. "Democracy for Polarized Committees: The Tale of Blotto's Lieutenants," Games and Economic Behavior, Elsevier, vol. 106(C), pages 239-259.
    3. Kai A. Konrad, 2011. "Strategie Aspects of Fighting in Alliances," Working Papers strategie_aspects_of_figh, Max Planck Institute for Tax Law and Public Finance.
    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. Kai A. Konrad & Florian Morath, 2018. "To Deter Or To Moderate? Alliance Formation In Contests With Incomplete Information," Economic Inquiry, Western Economic Association International, vol. 56(3), pages 1447-1463, July.
    6. Ke, Changxia & Konrad, Kai A. & Morath, Florian, 2013. "Brothers in arms – An experiment on the alliance puzzle," Games and Economic Behavior, Elsevier, vol. 77(1), pages 61-76.
    7. Michael Perry & Hadi El-Amine, 2019. "Computational Efficiency in Multivariate Adversarial Risk Analysis Models," Decision Analysis, INFORMS, vol. 16(4), pages 314-332, December.
    8. AmirMahdi Ahmadinejad & Sina Dehghani & MohammadTaghi Hajiaghayi & Brendan Lucier & Hamid Mahini & Saeed Seddighin, 2019. "From Duels to Battlefields: Computing Equilibria of Blotto and Other Games," Management Science, INFORMS, vol. 44(4), pages 1304-1325, November.
    9. repec:pit:wpaper:509 is not listed on IDEAS
    10. Duffy, John & Matros, Alexander, 2017. "Stochastic asymmetric Blotto games: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 88-105.
    11. Herbst, Luisa & Konrad, Kai A. & Morath, Florian, 2015. "Endogenous group formation in experimental contests," European Economic Review, Elsevier, vol. 74(C), pages 163-189.
    12. Bozbay, Irem & Vesperoni, Alberto, 2018. "A contest success function for networks," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 404-422.
    13. Goerke, Laszlo & Neugart, Michael, 2015. "Lobbying and dismissal dispute resolution systems," International Review of Law and Economics, Elsevier, vol. 41(C), pages 50-62.
    14. James W. Boudreau & Lucas Rentschler & Shane Sanders, 2019. "Stag hunt contests and alliance formation," Public Choice, Springer, vol. 179(3), pages 267-285, June.
    15. Konrad, Kai A., 2010. "Dynamic contests," Discussion Papers, Research Professorship & Project "The Future of Fiscal Federalism" SP II 2010-10, WZB Berlin Social Science Center.
    16. Kai Konrad, 2012. "Information alliances in contests with budget limits," Public Choice, Springer, vol. 151(3), pages 679-693, June.
    17. 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.
    18. K.J.M. De Jaegher & B. Hoyer, 2012. "Cooperation and the common enemy effect," Working Papers 12-24, Utrecht School of Economics.

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    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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