We examine prosodic entrainment in cooperative game dialogs for new feature sets describing register, pitch accent shape, and rhythmic aspects of utterances. For these as well as for established features we present entrainment profiles to detect within- and across-dialog entrainment by the speakers' gender and role in the game. It turned out, that feature sets undergo entrainment in different quantitative and qualitative ways, which can partly be attributed to their different functions. Furthermore, interactions between speaker gender and role (describer vs. follower) suggest gender-dependent strategies in cooperative solution-oriented interactions: female describers entrain most, male describers least. Our data suggests a slight advantage of the latter strategy on task success.