Reinforcement learning in the guarding a territory game

In this paper, we investigate the use of reinforcement learning to train the players in the game of guarding a territory. The game is played in the continuous domain. There are two players in the game: an invader and a guard. In our formulation, we set the guard to be 30 percent faster than the invader. We make the assumption that the players have no a priori knowledge of their optimal behavior. Therefore, the players will obtain these after learning. In other words, both players are simultaneously learning in the game. We introduce the Apollonius circle approach to determine the optimal solution of the guarding a territory game, when the guard is faster than the invader. We make use of the optimal solution of the game determined using the Apollonius circle approach to evaluate the learning performance of the players. We present simulation results and discuss the effectiveness of the approach.