The high potential of superquadrics as modeling elements for image segmentation tasks has been pointed out for years in the computer vision community. In this work, we employ superquadrics as modeling elements for multiple object segmentation in range images. Segmentation is executed in two stages: First, a hypothesis about the values of the segmentation parameters is generated. Second, the hypothesis is refined locally. In both stages, object boundary and region information are considered. Boundary information is derived via model-based edge detection in the input range image. Hypothesis generation uses boundary information to isolate image regions that can be accurately described by superquadrics. Within hypothesis refinement, a game-theoretic framework is used to fuse the two information sources by associating an objective function to each information source. Iterative optimization of the two objective functions in succession, outputs a precise description of all image objects. We demonstrate experimentally that this approach substantially improves the most established method in superquadric segmentation in terms of accuracy and computational efficiency. We demonstrate the applicability of our segmentation framework in real-world applications by constructing a novel robotic system for automatic unloading of jumbled box-like objects from platforms.