Optimal Pricing Under Vertical and Horizontal Interaction Structures for IoT Networks

An Internet of Things (IoT) system can include several different types of service providers, who sell IoT service, network service, and computation service to customers, either jointly or separately. The complicated coupling among these providers in terms of pricing and service decisions is an under-explored research area, the understanding of which is critical to the success of IoT networks. This paper studies the impact of the provider interaction structures on the overall IoT system with massive heterogeneous customers. Specifically, we consider three interaction structures: coordinated, vertically-uncoordinated, and horizontally-uncoordinated structures. Despite the challenging non-convex optimization problems involved in modeling and analyzing these structures, we successfully obtain the closed-form optimal pricing strategies of providers in each interaction structure. We prove that the coordinated structure is better than two uncoordinated structures for both providers and customers, as it avoids selfish price markup behaviors in uncoordinated structures. When customers' demand variance is large and utility-cost ratio is medium, vertically-uncoordinated structure is better than horizontal one for both providers and customers, due to the complementary providers' competition in horizontally-uncoordinated structure. Counter-intuitively, we identify that providers' optimal prices do not change with their costs at the critical point of customers' full participation in the vertically-uncoordinated structure.