Reinforcement learning enables mobile robots to make fast and scalable navigation decisions in constrained human-shared environments. However, directly extending single-robot approaches to multi-robot settings often fails to ensure safety and efficiency, especially under occlusions and out-of-distribution (OOD) scenarios, where individual robots may overlook potential risks or make inaccurate predictions. Leveraging cooperation effectively for both prediction and navigation remains a major challenge. We propose CoopUQ, a multi-robot social navigation framework that bridges uncertainty-aware cooperative occupancy forecasting and robust decision making. CoopUQ predicts future occupancy grid maps through cross-robot spatiotemporal feature fusion and further leverages forecasts and their uncertainty to guide policy via constrained multi-agent reinforcement learning, where the cost penalizes navigation through regions predicted to be occupied or highly uncertain. This design enables the policy to adapt its risk sensitivity under distribution shifts. Experimental results across multiple Unity3D-based simulation environments with both in-distribution and OOD settings, including diverse layouts, pedestrian densities, and rushing behavior, demonstrate improved prediction performance and safety over representative baselines. Real-robot experiments further demonstrate its robustness across various scenes. Our code and videos are available at https://coopuq.github.io/.

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