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

Sequential, nonzero-sum “Blotto”: Allocating defensive resources prior to attack 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Games and Economic Behavior Elsevier

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

Games and Economic Behavior, Volume 67 (2) – Nov 1, 2009

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Publisher
Elsevier
Copyright
Copyright © 2009 Elsevier Inc.
ISSN
0899-8256
D.O.I.
10.1016/j.geb.2009.03.011
Publisher site
See Article on Publisher Site

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.

Journal

Games and Economic BehaviorElsevier

Published: Nov 1, 2009

References

  • Discrete Colonel Blotto and general Lotto games
    Hart, S.
  • The Colonel Blotto game
    Roberson, B.

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