Non-linear programming approach to simulation of the general adversarial agents problem

The adversarial agents problem is a generalized game-theoretic problem in which a set of agents faces a set of adversarial agents of varying types and capabilities, and must plan and perform actions to try to accomplish a specified goal; instances of this problem are often conceived as military combat situations. In this paper, we formulate the general adversarial agents problem as a non-linear integer programming problem, and show how an optimizing solver can be used to generate strategies for instances of the problem, with examples to illustrate the approach. Finally, we discuss the usefulness of such a formulation for real-world problems, particularly in system modeling and simulation for verification of heuristic strategy and planning algorithms and approaches.