In this talk I will present some of our findings (in collaboration with the Bank of Canada) on using RL to approximate the policy rules of banks participating in a high-value payments system. The objective of the agents is to learn a policy function for the choice of amount of liquidity provided to the system at the beginning of the day. Individual choices have complex strategic effects precluding a closed form solution of the optimal policy, except in simple cases. We show that in a simplified two-agent setting, agents using reinforcement learning do learn the optimal policy that minimizes the cost of processing their individual payments. We also show that in more complex settings, both agents learn to reduce their liquidity costs. Our results show the applicability of RL to estimate best-response functions in real-world strategic games.