Solution of a differential game with geographically distributed resources

We present a computer tool for finding a local Nash solution to an adversarial game in which the units of two opposing teams are distributed over a large geographical area. The differential game consists of a quadratic payoff function and a set of ordinary differential equations describing the system dynamics of the unit distribution over a discretized geographical area. The optimum strategy for each team is determined using an iterative algorithm for finding a local Nash equilibrium solution for the game. Experimental results are presented that demonstrate the validity of this concept.