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For prediction of interacting agents' trajectories, we propose an end-to-end trainable architecture that hybridizes neural nets with game-theoretic reasoning, has interpretable intermediate representations, and transfers to downstream decision making. It uses a net that reveals preferences from the agents' past joint trajectory, and a differentiable implicit layer that maps these preferences to local Nash equilibria, forming the modes of the predicted future trajectory. Additionally, it learns an equilibrium refinement concept. For tractability, we introduce a new class of continuous potential games and an equilibrium-separating partition of the action space. We provide theoretical results for explicit gradients and soundness. In experiments, we evaluate our approach on two real-world data sets, where we predict highway drivers' merging trajectories, and on a simple decision-making transfer task.