A Game-Theoretic Analysis of Complementarity, Substitutability and Externalities in Cloud Services

In cloud computing, cloud services can be allocated to users upon requests in an on-demand basis. Heterogeneous cloud service providers may join the cloud systems to serve various types of users. Cloud services can be complementary or substitutable. For the complementary services, users may request for a bundle of the services, e.g., CPU and storage, to gain higher benefit from requesting them alone. The substitutable services have similar functionalities to serve users, e.g., different cloud database services, obtaining one of them can replace another one. Furthermore, the users of the cloud systems also influence each other because of externalities, particularly, network effect and congestion effect. From the perspective of each user, the existence of other users may introduce positive or negative impacts on the user utility, in the case of network and congestion effects, respectively. In this work, the participants in the cloud systems are treated as social enabled rational individuals. We model the complementarity, substitutability and externalities in cloud services by employing a multiple-leader multiple- follower Stackelberg game approach, including a two-stage service transaction process where service providers and users make their transaction decisions in a distributed manner. The analytical expressions of equilibria, service pricing strategies, and service allocations are derived with numerical results. We also find in the numerical results that both collusive and competitive service pricing schemes may lead to the optimized provider and user performances simultaneously.