Envelopment strategies and contract design of two-sided platforms

Platform envelopment, which describes the embedding of one platform into another platform, is widely adopted by platforms with network effects. The strategic use of platform envelopment is determined by the tradeoff between the benefits of sharing existing users and inconvenience of using the embedded platform. This study investigates when the pure envelopment strategy (PES), mixed envelopment strategy (MES), or no envelopment strategy (NES) should be adopted and examines several coordination schemes for the platforms. A centralized decision-making case and a decentralized decision-making case are first formulated and compared. The results show that NES is the only equilibrium solution under a decentralized decision-making case and the cooperation between the two platforms can lead to higher profit of both platforms by adopting the PES or the MES. We then propose a partial equity ownership (PEO) contract, a proportional fee (PF) contract, and a fixed fee (FF) contract to coordinate the system, benefiting both platforms. The PES or the MES may be the equilibrium strategy under a PEO contract, whereas the MES is the only equilibrium strategy under a PF or an FF contract. This study finds that the adoption of a PEO contract will lead to higher surplus of consumers and providers, and social welfare. In addition, we find that only PEO contract may perfectly coordinate platforms to achieve the same total profit as that under the centralized decision-making case, while PF and FF contracts cannot.