## Abstract

This paper investigates efficient computation schemes for allocating two defensive resources to multiple sites to protect against possible attacks by an adversary. The availability of the two resources is constrained and the effectiveness of each may vary over the sites. The problem is formulated as a two-person zero-sum game with particular piecewise linear utility functions: the expected damage to a site that is attacked linearly decreases in the allocated resource amounts up to a point that a site is fully protected. The utility of the attacker, equivalently the defender's disutility, is the total expected damage over all sites. A fast algorithm is devised for computing the game's Nash equilibria; it is shown to be more efficient in practice than both general purpose linear programming solvers and a specialized method developed in the mid-1980s. To develop the algorithm, optimal solution properties are explored.

Original language | English |
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Pages (from-to) | 218-229 |

Number of pages | 12 |

Journal | Computers and Operations Research |

Volume | 78 |

DOIs | |

State | Published - 1 Feb 2017 |

### Bibliographical note

Publisher Copyright:© 2016 Elsevier Ltd

## Keywords

- Large scale optimization
- Multiple resources
- Nash equilibria
- Resource allocation
- Resource substitution