  Multi-agent reinforcement learning (MARL) has become a significant research
topic due to its ability to facilitate learning in complex environments. In
multi-agent tasks, the state-action value, commonly referred to as the Q-value,
can vary among agents because of their individual rewards, resulting in a
Q-vector. Determining an optimal policy is challenging, as it involves more
than just maximizing a single Q-value. Various optimal policies, such as a Nash
equilibrium, have been studied in this context. Algorithms like Nash Q-learning
and Nash Actor-Critic have shown effectiveness in these scenarios. This paper
extends this research by proposing a deep Q-networks (DQN) algorithm capable of
learning various Q-vectors using Max, Nash, and Maximin strategies. The
effectiveness of this approach is demonstrated in an environment where dual
robotic arms collaborate to lift a pot.
