Since a large variety of digital games have been used in many fields for educational purposes, their real functions in learning have caught much attention as well. This study first defines learning characteristics of problem-solving digital games and their corresponding cognitive levels, then designs and develops a problem-solving game in accordance to the criteria. Tasks in the game context are inter-related to each other so that players need to critically and creatively think about problem solutions. Learners' task analyses are performed to observe four elementary learners' gaming paths, behaviors and cognitive activities, individually and collaboratively. System documentation, video recording, researcher observation, and interviews are conducted to analyze learners' learning strategies and their cognitive performance during the gaming process. The research results show that different collaboration models, strategies, as well as atmospheres can greatly influence the performances of its members. In collaboration, each individual can have better learning effectiveness. Participants in positive and favorable collaborative relationships, regardless of the members' individual temperaments, can have much better cognitive performances. While group members are inter-dependent and have positive interactions, even slow-achievers have the possibility and opportunity to take the lead. (Contains 5 tables and 6 figures.)