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Systems defense games: Colonel blotto, command and control

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  • Martin Shubik
  • Robert James Weber

Abstract

The classical “Colonel Blotto” games of force allocation are generalized to include situations in which there are complementarities among the targets being defended. The complementarities are represented by means of a system “characteristic function,” and a valuation technique from the theory of cooperative games is seen to indicate the optimal allocations of defense and attack forces. Cost trade‐offs between systems defense and alternative measures, such as the hardening of targets, are discussed, and a simple example is analyzed in order to indicate the potential of this approach.

Suggested Citation

  • Martin Shubik & Robert James Weber, 1981. "Systems defense games: Colonel blotto, command and control," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(2), pages 281-287, June.
    • Handle: RePEc:wly:navlog:v:28:y:1981:i:2:p:281-287
    DOI: 10.1002/nav.3800280210
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    References listed on IDEAS

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    1. Martin Shubik & Robert J. Weber, 1978. "Competitive Valuation of Cooperative Games," Cowles Foundation Discussion Papers 482, Cowles Foundation for Research in Economics, Yale University.
    2. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    3. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-968, October.
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    Cited by:

    1. Mohammad E. Nikoofal & Jun Zhuang, 2012. "Robust Allocation of a Defensive Budget Considering an Attacker's Private Information," Risk Analysis, John Wiley & Sons, vol. 32(5), pages 930-943, May.
    2. Martin Shubik, 1984. "The Cooperative Form, the Value and the Allocation of Joint Costs and Benefits," Cowles Foundation Discussion Papers 706, Cowles Foundation for Research in Economics, Yale University.
    3. 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.
    4. Vicki Bier & Santiago Oliveros & Larry Samuelson, 2007. "Choosing What to Protect: Strategic Defensive Allocation against an Unknown Attacker," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(4), pages 563-587, August.
    5. Denter, Philipp, 2020. "Campaign contests," European Economic Review, Elsevier, vol. 127(C).
    6. Sergio Monsalve, 2002. "Teoría de juegos: ¿hacia dónde vamos? (60 años después de von Neumann y Morgenstern)," Revista de Economía Institucional, Universidad Externado de Colombia - Facultad de Economía, vol. 4(7), pages 114-130, July-Dece.
    7. Martin Shubik, 1987. "Game Theory. Models of Strategic Behavior and Nuclear Deterrence," Cowles Foundation Discussion Papers 829, Cowles Foundation for Research in Economics, Yale University.
    8. Brian Roberson & Oz Shy, 2021. "Costly force relocation in the Colonel Blotto game," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 39-52, April.
    9. Edouard Kujawski, 2015. "Accounting for Terrorist Behavior in Allocating Defensive Counterterrorism Resources," Systems Engineering, John Wiley & Sons, vol. 18(4), pages 365-376, July.
    10. Shy, Oz, 2021. "Multimarket lobbying with reserves," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 106-112.
    11. Boix-Adserà, Enric & Edelman, Benjamin L. & Jayanti, Siddhartha, 2021. "The multiplayer Colonel Blotto game," Games and Economic Behavior, Elsevier, vol. 129(C), pages 15-31.
    12. 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.
    13. Deutsch, Yael, 2021. "A polynomial-time method to compute all Nash equilibria solutions of a general two-person inspection game," European Journal of Operational Research, Elsevier, vol. 288(3), pages 1036-1052.
    14. Cary Deck & Roman Sheremeta, 2010. "Fight or Flight? Defending Against Sequential Attacks in the Game of Siege," Working Papers 10-20, Chapman University, Economic Science Institute.
    15. Russell Golman & Scott Page, 2009. "General Blotto: games of allocative strategic mismatch," Public Choice, Springer, vol. 138(3), pages 279-299, March.
    16. 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.
    17. Enric Boix-Adser`a & Benjamin L. Edelman & Siddhartha Jayanti, 2020. "The Multiplayer Colonel Blotto Game," Papers 2002.05240, arXiv.org, revised May 2021.
    18. Martin Shubik, 1998. "Game Theory, Complexity and Simplicity. Part III: Critique and Prospective," Cowles Foundation Discussion Papers 1184, Cowles Foundation for Research in Economics, Yale University.
    19. Lever Guzmán Carlos, 2010. "Strategic Spending in Voting Competitions with Social Networks," Working Papers 2010-16, Banco de México.

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