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

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  • Powell, Robert
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6WFW-4W15KT7-2/2/f21b67962d52772c757eb65e1ef04d6c
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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 67 (2009)
    Issue (Month): 2 (November)
    Pages: 611-615

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    Handle: RePEc:eee:gamebe:v:67:y:2009:i:2:p:611-615

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    Web page: http://www.elsevier.com/locate/inca/622836

    Related research

    Keywords: Blotto Minmax Defense Terrorism;

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    Cited by:
    1. Wenzel, Lars & Wolf, André, 2013. "Protection against major catastrophes: An economic perspective," HWWI Research Papers 137, Hamburg Institute of International Economics (HWWI).
    2. 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.
    3. John Duffy & Alexander Matros, 2013. "Stochastic Asymmetric Blotto Games: Theory and Experimental Evidence," Working Papers 509, University of Pittsburgh, Department of Economics, revised Nov 2013.
    4. S. Goyal & A. Vigier, 2013. "Attack, Defense and Contagion in Networks," Cambridge Working Papers in Economics 1327, Faculty of Economics, University of Cambridge.

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