Calibration of Shared Equilibria in General Sum Partially Observable Markov Games
This work addresses the challenge of making multi-agent systems practical for modeling real-world systems by ensuring their emergent behaviors match external targets, though it appears incremental as it builds on existing parameter-sharing methods.
This paper tackles the problem of training multi-agent systems to achieve realistic equilibria by introducing the concept of Shared equilibrium in general sum partially observable Markov games and developing a dual-Reinforcement Learning approach to calibrate these equilibria to real-world targets, applying it to an n-player market example.
Training multi-agent systems (MAS) to achieve realistic equilibria gives us a useful tool to understand and model real-world systems. We consider a general sum partially observable Markov game where agents of different types share a single policy network, conditioned on agent-specific information. This paper aims at i) formally understanding equilibria reached by such agents, and ii) matching emergent phenomena of such equilibria to real-world targets. Parameter sharing with decentralized execution has been introduced as an efficient way to train multiple agents using a single policy network. However, the nature of resulting equilibria reached by such agents has not been yet studied: we introduce the novel concept of Shared equilibrium as a symmetric pure Nash equilibrium of a certain Functional Form Game (FFG) and prove convergence to the latter for a certain class of games using self-play. In addition, it is important that such equilibria satisfy certain constraints so that MAS are calibrated to real world data for practical use: we solve this problem by introducing a novel dual-Reinforcement Learning based approach that fits emergent behaviors of agents in a Shared equilibrium to externally-specified targets, and apply our methods to a n-player market example. We do so by calibrating parameters governing distributions of agent types rather than individual agents, which allows both behavior differentiation among agents and coherent scaling of the shared policy network to multiple agents.