A Raid-Type War-Game Model Based on a Discrete Multi-Weapon Lanchester's Law

We propose a war-game model that is appropriate for a raid-type warfare in which, a priori, the maneuver of the attacker is relatively certain. The model is based on a multi-weapon extention of the Lanchester's law. Instead of a continuous time dynamic game with the differential equations from the Lanchester's law, however, we adopt a multi-period model relying on a time-discretization of the Lanchester's law. Despite the obvious limitation that two players make a move only on the discrete time epochs, the pragmatic model has a manifold justification. The existence of an equilibrium is readily established by its equivalence to a finite zero-sum game, the existence of whose equilibrium is, in turn, well-known to be no other than the LP-duality. It implies then that the war-game model dictates optimal strategies for both players under the assumption that any strategy choice of each player will be responded by a best strategy of her opponent. The model, therefore, provides a sound ground for finding an efficient reinforcement of a defense system that guarantees peaceful equilibria.