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Sequential, nonzero-sum "Blotto": Allocating defensive resources prior to attack

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  • Powell, Robert

Abstract

The strategic allocation of resources across multiple fronts has long been studied in the context of Blotto games in which two players simultaneously select their allocations. However many allocation problems are sequential. For example, a state trying to defend against a terrorist attack generally allocates some or all of its resources before the attacker decides where to strike. This paper studies the allocation problem confronting a defender who must decide how to distribute limited resources across multiple sites before an attacker chooses where to strike. Unlike many Blotto games which only have very complicated mixed-strategy equilibria, the sequential, nonzero-sum "Blotto" game always has a very simple pure-strategy subgame perfect equilibrium. Further, the defender always plays the same pure strategy in any equilibrium, and the attacker's equilibrium response is generically unique and entails no mixing. The defender minmaxes the attacker in equilibrium even though the game is nonzero-sum, and the attacker strikes the site among its best replies that minimizes the defender's expected losses.

Suggested Citation

  • Powell, Robert, 2009. "Sequential, nonzero-sum "Blotto": Allocating defensive resources prior to attack," Games and Economic Behavior, Elsevier, vol. 67(2), pages 611-615, November.
  • Handle: RePEc:eee:gamebe:v:67:y:2009:i:2:p:611-615
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    References listed on IDEAS

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    Cited by:

    1. Nakao, Keisuke, 2017. "Denial vs. Punishment: Strategies Shape War, but War Itself Affects Strategies," MPRA Paper 81418, University Library of Munich, Germany.
    2. repec:pit:wpaper:509 is not listed on IDEAS
    3. repec:eee:jeborg:v:139:y:2017:i:c:p:88-105 is not listed on IDEAS
    4. repec:eee:reensy:v:136:y:2015:i:c:p:35-46 is not listed on IDEAS
    5. Sanjeev Goyal & Adrien Vigier, 2014. "Attack, Defence, and Contagion in Networks," Review of Economic Studies, Oxford University Press, vol. 81(4), pages 1518-1542.
    6. Kjell Hausken, 2014. "Choosing what to protect when attacker resources and asset valuations are uncertain," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 3, pages 23-44.
    7. Wenzel, Lars & Wolf, André, 2013. "Protection against major catastrophes: An economic perspective," HWWI Research Papers 137, Hamburg Institute of International Economics (HWWI).
    8. repec:cai:repdal:redp_273_0307 is not listed on IDEAS
    9. repec:spr:annopr:v:236:y:2016:i:1:d:10.1007_s10479-014-1722-3 is not listed on IDEAS
    10. Shan, Xiaojun & Zhuang, Jun, 2013. "Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defender–attacker game," European Journal of Operational Research, Elsevier, vol. 228(1), pages 262-272.
    11. 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.
    12. Ur Rehman Faiz, 2015. "The Spatial Analysis of Terrorism in Pakistan," Asian Journal of Law and Economics, De Gruyter, vol. 6(2), pages 125-165, October.
    13. Oléron Evans, Thomas P. & Bishop, Steven R., 2013. "Static search games played over graphs and general metric spaces," European Journal of Operational Research, Elsevier, vol. 231(3), pages 667-689.

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    Keywords

    Blotto Minmax Defense Terrorism;

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