  We investigate the challenge of multi-agent deep reinforcement learning in
partially competitive environments, where traditional methods struggle to
foster reciprocity-based cooperation. LOLA and POLA agents learn
reciprocity-based cooperative policies by differentiation through a few
look-ahead optimization steps of their opponent. However, there is a key
limitation in these techniques. Because they consider a few optimization steps,
a learning opponent that takes many steps to optimize its return may exploit
them. In response, we introduce a novel approach, Best Response Shaping (BRS),
which differentiates through an opponent approximating the best response,
termed the "detective." To condition the detective on the agent's policy for
complex games we propose a state-aware differentiable conditioning mechanism,
facilitated by a question answering (QA) method that extracts a representation
of the agent based on its behaviour on specific environment states. To
empirically validate our method, we showcase its enhanced performance against a
Monte Carlo Tree Search (MCTS) opponent, which serves as an approximation to
the best response in the Coin Game. This work expands the applicability of
multi-agent RL in partially competitive environments and provides a new pathway
towards achieving improved social welfare in general sum games.
