# Optimal Pricing in a Rented 5G Infrastructure Scenario with Sticky Customers
## 6 Results  
After ruling out the possibility of a Nash equilibrium for prices in Section 5, we can explore the three scenarios set out at the end of the previous section, where prices are set by one of the stakeholders (the MNO, the MVNOs, and the regulatory authority). Here, we report each scenario's prices and profits considering the impact of the bandwidth allotted to customers and the stickiness factor. We will denote each price-setting scenario by using a specific superscript: \"\(\circ\)\" when the owner (MNO) acts as the price setter, \"r\" when the renters (MVNOs) set the price, and \"SW\" when price setting is left to the regulator. For simplicity, when the renters set prices, we assume that they make the same choice, i.e., they all set the same price. Consequently, we will adopt the notation \(p_{h}^{(k)}\) for prices, which denotes the price offered by operator \(h\) when the price-setting scenario \(k\) applies. For example, \(p_{\text{MNO}}^{(\text{SW})}\) will be the price offered by the owner and set by the regulator. Similarly, we will adopt the notation \(\Pi_{h}^{(k)}\) for profits. For the purpose of considering different competition levels, in the following, we consider three cases of competition: monopoly, i.e., no competition (\(N_{R}=0\)); a single MVNO (\(N_{R}=1\)), and three MVNOs (\(N_{R}=3\)). This is largely in line with the real world. Four operators are currently present in the UK (see [[https://www.rcruireless.com/2021/0310/5g/the-latest-on-the-status-of-the-uks-5g-deployments](https://www.rcruireless.com/2021/0310/5g/the-latest-on-the-status-of-the-uks-5g-deployments)]([https://www.rcruireless.com/2021/0310/5g/the-latest-on-the-status-of-the-uks-5g-deployments](https://www.rcruireless.com/2021/0310/5g/the-latest-on-the-status-of-the-uks-5g-deployments)) (accessed on 16 February 2023)), whereas 135 operators have launched 5G services in 58 countries according to the latest report of the Global Mobile Suppliers Association (GSA) by [62], which leads to an average of 2.3 operators per country. Hence, our choice lies within those two values. We have considered the parameter values shown in Table 1. Of course, those are the values for each parameter when that parameter is held constant. In the case of bandwidth, e.g., we may wish to see the effect of changing the bandwidth allowance to each customer on prices and profits. The values shown in Table 1 have been set either on the basis of the literature or postulated as educated guesses. The values considered for \(C_{0}\) and \(m\) have been derived from those reported in [44]. The bandwidth value for \(B\) is intermediate among those considered in [44]. The OPEX/CAPEX ratio \(\alpha\) lies in the range identified in Section 4.1, i.e., between 30% and 75%. The values for the fraction of CAPEX and OPEX bore by MVNOs (\(\beta_{i}\) and \(\eta_{i}\)) are educated guess derived from what is reported in [63], who report CAPEX and OPEX savings due to infrastructure sharing, where savings in the 25-48.6% range are reported for CAPEX and savings in the 14.9-19.9% range are reported for OPEX. Because \(\beta_{i}\) and \(\eta_{i}\) may be seen as the complement to 100% of savings, and savings from not deploying the infrastructure (as for an MVNO) are surely larger than those from sharing it, we can expect \(\beta_{i}<100-48.6=51.4\%\) and \(\eta_{i}<100-19.9=80.1\%\). The values we have employed obey those inequalities. We further remark that we preserve the ordering relationship \(\beta_{i}<\eta_{i}\) as resulting from the data shown in [63], i.e., that savings in CAPEX are larger than savings in OPEX. The values for the renting fee is an educated guess resulting from the business relationship observed between MNOs and MVNOs. The quasi elasticity of the basin penetration \(z\) has been chosen after considering that an average price of 350% with 80% penetration would lead to \(z=0.00064\).