Contract type of complementary product and service with quantity decisions

As the popularity of service-dominant logic, it is agreeable that service becomes new engine of business. Since many firms position their focuses on service, the traditional contracts are no longer suitable and many conflicts emerge between supply chain members. Indeed, the firm who provides service is willing to capture all the profit from service, while its partner who supplies product has incentive to share. In practice, firms have tried different contracts to coordinate their preferences, but sometimes result in problems. Motivated by the practice in the wireless industry, we consider a supply chain consisting of a handset vendor and a service provider and facing heterogeneous consumers. We develop a game theoretical model, characterize the two widely used contracts to deliver complementary product and service, compare the performances, and derive firms' preferences over these contracts. We find that revenue sharing contracts lead to larger market coverage than wholesale price contracts in general. However, the revenue sharing contract could be agreeable by both firms if and only if consumers are not too homogeneous; otherwise, the service provider has incentive to switch to the wholesale price contract. Moreover, no matter which contract is adopted, firms serve the whole market if and only if consumers are not too heterogeneous; otherwise, low-valuation consumers will be given up.