Allocating multiple defensive resources in a zero-sum game setting

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

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume225
Issue number1
DOIs
StatePublished - Feb 2015

Keywords

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

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research

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