# Optimal Pricing in a Rented 5G Infrastructure Scenario with Sticky Customers
## 2 Literature Review
A different view of the resources to be shared was considered in [21], where the authors dealt with caching space, which becomes a limited resource due to the exponential growth of mobile data and video consumption. They studied a multi-Stackelberg game between multiple mobile network operators (MNOs) (which act as leaders in the game) and several content providers (which act as followers). In the first step, the multi-leader Stackelberg game leads to definition of the prices that MNOs charge content providers. In the second step, a multi-follower Cournot game between content providers leads to definition of the content cached at the base stations of the mobile network operators. The strategic leverage is the price that mobile network operators set and the quantity of content that each content provider will cache. Instead, a scenario where two virtual network operators compete, sharing the infrastructure provided by a single provider and offering service to end IoT users, was studied in [22]. The authors proposed a two-stage Stackelberg game, where the two virtual operators first try to maximize their profits by setting the optimal network service prices, and then IoT users make select the network service based on performance and prices. Though network sharing has been depicted as a sharp move with respect to fully replicated networks, several shades are possible. Different degrees of sharing were explored in [23], and they were compared with the aim of optimizing efficiency. Several papers have focused on costs only, which is, however, the strongest spur towards adopting a network-sharing approach. An evaluation of architecture costs (capital and operational) was conducted in [24]. A detailed analysis of all the components and an evaluation of the net present values of capital expenses was provided in [25]. In [26], a 5G smart light pole network was considered, and a model was proposed to estimate the total deployment cost, including the capital and operational expenses. We now turn to consideration of papers that deal with a scenario similar to ours, where MNOs and MVNOs compete for end customers. A similar approach to ours was employed in [27], where a small cell operator leases the spectrum from the macro cell operator. The scenario is monopolistic at both levels (instead, we consider competition between virtual service providers). The users' utility function is sensitive to both the service price and the expected throughput (i.e., the network performance), whereas we include several aspects--not just performance--in the demand function. In [28], direct competition between operators was considered in a strategic business model where both the infrastructure owner and the virtual operator compete for end customers by offering different prices. Instead of considering the bandwidth provided to customers, they considered the quality of service. In addition to that, their model also differs from ours in that they did not consider costs and did not include the stickiness of customers in the demand function. A different kind of B2B service relationship was considered in [29], where a backup reservation scheme to cover for excess-demand needs was considered in place of the fixed provisioning agreement considered in our paper. Although most models consider the demand posed by users, in [30] the demand was represented by slice tenants, which act as agents participating in auctions. Their bids are updated after each auction round to maximize their payoff function. A reversed scenario, where the mobile network operator acts as a customer of local (micro) operators owning the infrastructure, was examined in [31], where the impact of competition on the wholesale prices paid by the MNO to the micro-operator was examined.