Multi-Agent Systems (MAS) are a form of distributed intelligence, where multiple autonomous agents act in a common environment. Numerous complex, real world systems have been successfully optimised using Multi-Agent Reinforcement Learning (MARL) in conjunction with the MAS framework. In MARL agents learn by maximising a scalar reward signal from the environment, and thus the design of the reward function directly affects the policies learned. In this work, we address the issue of appropriate multi-agent credit assignment in stochastic resource management games. We propose two new Stochastic Games to serve as testbeds for MARL research into resource management problems: the Tragic Commons Domain and the Shepherd Problem Domain. Our empirical work evaluates the performance of two commonly used reward shaping techniques: Potential-Based Reward Shaping and difference rewards. Experimental results demonstrate that systems using appropriate reward shaping techniques for multi-agent credit assignment can achieve near optimal performance in stochastic resource management games, outperforming systems learning using unshaped local or global evaluations. We also present the first empirical investigations into the effect of expressing the same heuristic knowledge in state- or action-based formats, therefore developing insights into the design of multi-agent potential functions that will inform future work.
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