Construction of Barrier Surfaces in Mutual Attack-Defense Games

In this paper, a variant of the target defense game is introduced, which involves two equal-speed agents and two targets. The agents do not possess a distinct role as either the defender or the intruder. Rather, each agent is tasked with protecting its own target while simultaneously attempting to breach the opponent’s target. This paper proposes a solution to the Game of Kind through the construction of barrier surfaces, which divide the space into two winning regions and a confronting region. The proposed optimal strategies ensure that the values of the barrier functions remain unchanged during the game. Finally, some simulations are studied to verify the effectiveness of the proposed optimal strategies. The game in this paper can provide a basis for more practical problems involving adversarial games, such as security systems and racing.