: This paper introduces a reinforcement learning technique with an internal reward for a multi-agent cooperation task. The proposed methods is an extension of Q-learning which changes the ordinary (external) reward to the internal reward for agent-cooperation. Specifically, we propose here two Q-learning methods, both of which employ the internal reward for the less or no communication. To guarantee the effectiveness of the proposed methods, we theoretically derived the mechanisms that solve the following questions: (1) how the internal rewards should be set to guarantee the cooperation among the agents under the condition of less and no communication; and (2) how the values of the cooperative behaviors types (i.e., the varieties of the cooperative behaviors of the agents) should be updated under the condition of no communication. The intensive simulations on the maze problem for the agent-cooperation task have been revealed that our two proposed methods successfully enable the agents to acquire their cooperative behaviors even in less or no communication, while the conventional method (Q-learning) always fails to acquire such behaviors.

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This study discusses important factors for zero communication, multi-agent cooperation by comparing different modified reinforcement learning methods. The two learning methods used for comparison were assigned different goal selections for multi-agent cooperation tasks. The first method is called Profit Minimizing Reinforcement Learning (PMRL); it forces agents to learn how to reach the farthest goal, and then the agent closest to the goal is directed to the goal. The second method is called Yielding Action Reinforcement Learning (YARL); it forces agents to learn through a Q-learning process, and if the agents have a conflict, the agent that is closest to the goal learns to reach the next closest goal. To compare the two methods, we designed experiments by adjusting the following maze factors: (1) the location of the start point and goal; (2) the number of agents; and (3) the size of maze. The intensive simulations performed on the maze problem for the agent cooperation task revealed that the two methods successfully enabled the agents to exhibit cooperative behavior, even if the size of the maze and the number of agents change. The PMRL mechanism always enables the agents to learn cooperative behavior, whereas the YARL mechanism makes the agents learn cooperative behavior over a small number of learning iterations. In zero communication, multi-agent cooperation, it is important that only agents that have a conflict cooperate with each other.

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