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Games are an increasingly useful tool for training and testing learning algorithms. Recent examples include GANs, AlphaZero and the AlphaStar league. However, multi-agent learning can be extremely difficult to predict and control. Learning dynamics can yield chaotic behavior even in simple games. In this paper, we present basic mechanism design tools for constructing games with predictable and controllable dynamics. We present a robust framework for dimensionality reduction arguments in large network games.

Robust Self-organization in Games: Symmetries, Conservation Laws and Dimensionality Reduction