A target defence-intrusion game with considering the obstructive effect of target

This paper considers the problem of a defender agent to guard the target area being attacked by a hostile agent. There are two different agents-intruder and defender here. The purpose of the defender is to prevent the intruder from approaching the target and if possible, catch the intruder. As the guardian object of the defender, the target area also obstructs its free movement. Therefore, a new geometric method is proposed to solve the problem. Firstly, the winning zones are constructed for the agents using two different methods. When the defender's initial position is in the defender's winning zone, the defender can capture the intruder. When the initial position of the defender is in the winning zone of the intruder, the intruder can successfully attack the target. Subsequently, a method is proposed for determining the dominance region boundary under the influence of target obstruction. Also, the winner can be ascertained by observing whether the dominance region boundary intersects the target area. The optimal strategy is then given according to the different payoff functions. Finally, some examples show the effectiveness of the method. In addition, the conditions and limitations for applying this method to other convex targets are provided.