# Optimal Pricing in a Rented 5G Infrastructure Scenario with Sticky Customers
###### Abstract  
The ongoing deployment of 5G is accompanied by architecture and pricing decisions. Network sharing is a critical feature, allowing operators to reduce their costs, but introducing a mixed partnering/competition situation, where the infrastructure owner, renting out their infrastructure to virtual operators (who act as customers), also provides services to end customers, competing with virtual operators. Pricing is the leverage through which an optimal balance between the two roles is accomplished. However, pricing may not be the only variable affecting customers' choice, which may prefer (stick to) one operator for several reasons. In this paper, we formulate a game model to analyse the optimal pricing decisions for operators in the presence of such sticky behaviour of customers. After concluding that the game does not allow for a Nash equilibrium, we consider a case when one of the parties (the infrastructure owner, the virtual operators, or the regulator) is responsible for setting prices and analyse how operators' profits are impacted when price-setting powers are shifted among the parties. The scenario where the regulator sets prices leads to the lowest profits for the operators, even lower than when competitors set prices. mobile networks; 5G networks; competition; virtual operators; pricing +
Footnote †: journal:  
001860018600186001860018600186001860018600186001860018600186018600  
in advance of the actual arrival of customers (it has been shown that some access sites carry a very low portion of traffic that does not justify the full investment [11]). The goal of network sharing is to increase efficiency and reduce costs for the operators while also improving customer coverage and capacity. It has been claimed that network sharing can save up to 20% of the operational costs and even half of the infrastructure costs of passive radio access network (RAN) components [8]. The possibility of partially or fully using the infrastructure of other operators rather than deploying one's own has led to the birth of virtual operators [12], which can carve a profitable business model by bearing null or reduced capital and operational expenses [13]. However, the use of the same infrastructure by different operators poses a competition problem, because the infrastructure owner could serve end customers at the same time, playing the double role of provider/partner and competitor towards the renting (virtual) operators. In order for this business scenario to be sustainable, prices and the subsequent demand of customers for the services of the two groups of operators must be enough to allow for profitable operations for both parties. A significant body of literature has dealt with the problem of correct/optimal prices offered by a single operator. Only a few works (considered in detail in Section 2) have considered the case generated by network sharing of a double-sided market, where virtual operators are customers of the infrastructure provider and providers of end customers at the same time. Furthermore, very few works have dealt with the more specific scenario where the infrastructure provider also serves end customers, thus creating the competition mentioned above. In addition, the emphasis has been on prices, which have been considered to be the only leverage (beyond service quality in some cases) for attracting customers. However, despite higher prices, several factors may push a customer towards one of the providers, ranging from brand reputation to service coverage and ancillary services. Unfortunately, the literature has so far avoided the mathematical consideration of factors that act concurrently with and beyond prices. In this paper, we wish to fill that research gap by introducing a demand function that allows us to model customers' preferences and orientate their decisions in addition to prices. We call this function the stickiness function, because it models how relatively difficult it may be for an operator to attract a customer who is sticking to another operator that he/she prefers.