We analyse the economic interaction on the market for composed services. Typically, as providers of composed services, intermediaries interact on the sales side with users and on the procurement side with providers of single services. Thus, in how far a user request can be met often crucially depends on the prices and qualities of the different single services used in the composition. We study an intermediary who purchases two complementary single services and combines them. The prices paid to the service providers are determined by simultaneous multilateral Nash bargaining between the intermediary and the respective service provider. By using a function with constant elasticity of substitution (CES) to determine the quality of the composed service, we allow for complementary as well as substitutable degrees of the providers’ service qualities. We investigate quality investments of service providers and the corresponding evolution of the single service quality within a differential game framework.