<p>The article investigates the existence of a stable coalition structure in coalition partition games dealing with a system of distinct representatives. The system of distinct representatives, or the transversal, is a coalition of agents whose members represent different groups. An agent gains utility if he/she belongs to a transversal. The transversal value of a cooperative game with coalition structure is introduced to solve the coalition formation problem. It is demonstrated that any cooperative game has a partition that is simultaneously Nash stable, permutation stable, and total payoff maximization for the transversal value. The transversal value expresses the players’ payoff functions in the workgroup formation game and the game of chairpersons. A player’s payoff in the workgroup formation game is the monetary reward for the projects the player participated in. In the game of chairpersons, each player is interested in being the group’s leader. It is demonstrated that there exist stable coalition structures with a punctuality property in such games.</p>