Game Theoretic Model for the Optimal Disposition of Integrated Air Defense System Assets.

摘要

We examine the optimal allocation of Integrated Air Defense System (IADS) resources to protect a country's assets, formulated as a Defender-Attacker-Defender three-stage sequential, perfect information, zero-sum game between two opponents. We formulate a trilevel nonlinear integer program for this Defender-Attacker-Defender model and seek a subgame perfect Nash equilibrium, for which neither the defender nor the attacker has an incentive to deviate from their respective strategies. Such a trilevel formulation is not solvable via conventional optimization software and an exhaustive enumeration of the game tree based on the discrete set of strategies is intractable for large problem sizes. As such, we test and evaluate variants of a tree pruning algorithm and a customized heuristic, which we benchmark against an exhaustive enumeration. Our tests demonstrate that the pruning strategy is not e cient enough to scale up to a larger problem. We then demonstrate the scalability of the heuristic to show that the model can be applied to a realistic size problem.