Allocating multiple defensive resources in a zero-sum game setting

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 re- sources 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 mono- tonicity 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 struc- ture of solutions in such settings is compared to that of Nash equilibria.