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Despite its interpretability, applying game theory to real-world robotics, like automated driving, faces challenges such as unknown game parameters. To tackle these, we establish a connection between differential games, optimal control, and energy-based models, demonstrating how existing approaches can be unified under our proposed Energy-based Potential Game formulation. Building upon this, we introduce a new end-to-end learning application that combines neural networks for game-parameter inference with a differentiable game-theoretic optimization layer, acting as an inductive bias. 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