# Optimal Pricing in a Rented 5G Infrastructure Scenario with Sticky Customers
## 2 Literature Review  
Many papers have been devoted to the analysis of economic models for 5G networks. In most cases, the models have been employed to drive resource management, e.g., spec trum allocation or interference and power management. An excellent survey of those models is shown in [14]. Examples of applications in data markets are provided in [15; 16; 17]. In this section, we focus instead on pricing models where two-sided markets emerge, which is the specific topic of our paper. For each paper described in this survey, we will outline the major difference between in and our paper. We first consider papers where there is no direct competition between the two sides of the two-sided market. The roles of the two sides may vary. In some cases, they may be the owner of the infrastructure and the renters. In other cases, they may be the spectrum licensee and the spectrum leasers. In any case, the absence of direct competition means that end users are solely the customer of one of the parties, so the scenarios considered in these papers differ from ours, at least in this basic aspect, i.e., not considering the competition between infrastructure providers and virtual operators. In [18], a game model was proposed, where wireless resource providers (WRPs), mobile virtual network operators (MVNOs), and users all take part. The set of stakeholders is the same as in our model. WRPs act as providers of RF slices for MVNOs, which in turn sublease their resources to end users. MVNOs act as two-sided players, being customers for WRPs and providers for end users (as in our model). However, WRPs do not directly serve end users and do not compete with MVNOs for those users (contrary to what happens in our model). The game is arranged according to three layers, with WRPs announcing their prices to MVNOs in layer 1 to maximize their own utility, MVNOs announcing their prices to end users in layer 2 to maximize their own utility, and end users optimising their data rate in layer 3. The game model obeys the Stackelberg-like leader-follower scheme. Another scenario considering a monopolistic infrastructure provider (a small cell provider) and many virtual network service providers was considered in [19]. However, the competition occurs just among virtual providers who compete for end users based on their prices and services and aim to maximize their profits. The authors employed a hierarchical game model. In their model, end users select services, and the operators engage in an upper-level game based on their leasing and pricing strategies to satisfy the service requests of end users. In the lower level, a Stackelberg game takes place between users and virtual service providers, who play the role of Stackelberg leaders. A further layering of operators was considered in [20], where an infrastructure provider rents its infrastructure to a mobile virtual network operator, which in turn virtualizes the network resources, divides them into slices, and rents them to edge and cloud service providers. They then considered a B2B market made of a single infrastructure provider and a single virtual operator. The problem they dealt with is the maximisation of the social welfare of the ecosystem formed by the MVNO and all the edge and cloud providers. Another model considering a three-level hierarchy was proposed in [18], where a three-layer game is adopted based on the interactions between wireless resource providers, mobile virtual network operators, and their subscribed wireless users. The wireless resource providers sublease their wireless resources to virtual operators, which in turn try to attract more end-users. The resource provider wishes to maximize its utility. The virtual operators wish to maximize their revenues. Finally, end users wish to maximize their data rates by meeting the imposed quality of service requirements and budget constraints.