Allocating multiple defensive resources in a zero-sum game setting

B. Golany, N. Goldberg, U. G. Rothblum

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


This paper investigates the problem of allocating multiple defensive resources to protect multiple sites against possible attacks by an adversary. The effectiveness of the resources in reducing potential damage to the sites is assumed to vary across the resources and across the sites and their availability is constrained. The problem is formulated as a two-person zero-sum game with piecewise linear utility functions and polyhedral action sets. Linearization of the utility functions is applied in order to reduce the computation of the game’s Nash equilibria to the solution of a pair of linear programs (LPs). The reduction facilitates revelation of structure of Nash equilibrium allocations, in particular, of monotonicity properties of these allocations with respect to the amounts of available resources. Finally, allocation problems in non-competitive settings are examined (i.e., situations where the attacker chooses its targets independently of actions taken by the defender) and the structure of solutions in such settings is compared to that of Nash equilibria.

Original languageEnglish
Pages (from-to)91-109
Number of pages19
JournalAnnals of Operations Research
Issue number1
StatePublished - Feb 2012
Externally publishedYes

Bibliographical note

Funding Information:
The authors would like to thank Pelin Canbolat, Edward H. Kaplan, and Hanan Luss for comments. B. Golany and U.G. Rothblum were supported in part by the Daniel Rose Technion-Yale Initiative for Research on Homeland Security and Counter-Terrorism. N. Goldberg was supported in part by the Daniel Rose Technion-Yale Initiative for Research on Homeland Security, and Counter-Terrorism, the Center for Absorption in Science of the Ministry of Immigrant Absorption and the Council of Higher Education, State of Israel.

Publisher Copyright:
© 2012, Springer Science+Business Media, LLC.


  • Allocation monotonicity
  • Multiple resource allocation
  • Nash equilibria
  • Resource substitution


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