Team Coverage Games (TCGs) are a representation of cooperative games, where the value a coalition generates depends on both individual contributions of its members and synergies between them. The synergies are expressed in terms of the importance of the agents in various teams. TCGs model the synergy as a reduction in utility that occurs when team members are missing, causing the team not to achieve its full potential. We focus on the case where the utility reduction incured is a concave function of the importance of the missing team members and analyze the domain from a computational game theoretic perspective.