A game of deception

In this paper, we study the problem of persistent area denial, where aircraft are stationed in areas where a potential ground adversary may appear. The object of the aircraft is to detect the adversary´s arrival, and preempt the adversary´s attack. The adversary can use decoys to create false arrivals, thereby distracting the aircraft and potentially allowing completion of the attack. We formulate this problem as a two-person zero-sum dynamic game with discrete moves, and we study the solutions of this game under different information structures, corresponding to whether the adversary can observe the past decisions of the aircraft. Using dynamic programming, we develop closed-form feedback solutions for the players´ optimal strategies under the different information structures, and expressions for the minimax value of the game. Our results show that the use of decoys offers a decided advantage to the adversary when the actions of the aircraft are observed. However, this advantage is removed if the aircraft can prevent observation of its moves.