# Table 1 Symbols and parameters for mathematical formulations

Parameters Explanations
$${\mathcal{A}}_{\mathcal{D}}$$ The totally allocated spectrum resource for the $$\mathcal{D}$$
$${\mathcal{A}}_{\mathcal{D}}^{\mathfrak{B}}$$ The $$\mathcal{D}$$’s LTE spectrum amount
$${\mathcal{A}}_{\mathcal{D}}^{\mathcal{W}}$$ The $$\mathcal{D}$$’s WiFi spectrum amount
$$\mathfrak{B}$$ The LTE base station
$${\mathbb{B}}_{\mathcal{W}}$$ The $$\mathcal{W}$$’s IoT devices generated BESs
$${\mathbb{D}}$$ The set of IoT devices
$${\mathcal{D}}_{1\le j\le n}$$ The jth IoT device
$${\mathbb{G}}_{\mathfrak{B}}$$ The second phase bargaining game
$${\mathbb{G}}_{\mathcal{W}}^{\mathfrak{B}}$$ The first phase bargaining game
$${\mathbb{G}}_{\mathcal{W}}$$ The third phase bargaining game
$${\mathcal{J}}_{\mathcal{D}}$$ The $$\mathcal{D}$$’s strategy in the $${\mathbb{G}}_{\mathcal{W}}$$
$${\mathfrak{M}}_{\mathfrak{B}}^{t}$$ Total sum of $${\mathcal{T}}_{\mathcal{D}}$$ where $$\mathcal{D}\in {\mathbb{Q}}_{\mathfrak{B}}$$
$${\mathfrak{M}}_{\mathcal{W}}^{t}$$ Total sum of $${\mathcal{T}}_{\mathcal{D}}$$ where $$\mathcal{D}{\in {\mathbb{B}}}_{\mathcal{W}}$$
$${\mathcal{R}}_{\mathfrak{B}}$$ The $$\mathfrak{B}$$’s part of the $${\mathcal{S}}_{\mathfrak{B}}$$
$${\mathcal{R}}_{\mathcal{W}}$$ The $$\mathcal{W}$$’s part of the $${\mathcal{S}}_{\mathfrak{B}}$$
$${\Upsilon}_{\mathcal{D}}$$ The $$\mathcal{D}$$’s strategy to share the $${\mathcal{R}}_{\mathfrak{B}}$$ in the $${\mathbb{G}}_{\mathfrak{B}}$$
$${\mathcal{S}}_{\mathfrak{B}}$$ The licensed spectrum band of $$\mathfrak{B}$$
$${\mathcal{S}}_{\mathcal{W}}$$ The unlicensed spectrum band of $$\mathcal{W}$$
$${\mathcal{T}}_{\mathcal{D}}$$ The $$\mathcal{D}$$’s maximum spectrum requirement
$${\mathfrak{U}}_{\mathfrak{B}}\left(\cdot \right)$$ The $$\mathfrak{B}$$’s utility function in the $${\mathbb{G}}_{\mathcal{W}}^{\mathfrak{B}}$$
$${\mathfrak{U}}_{\mathcal{W}}\left(\cdot \right)$$ The $$\mathcal{W}$$’s utility function in the $${\mathbb{G}}_{\mathcal{W}}^{\mathfrak{B}}$$
$${U}_{\mathcal{D}}\left(\cdot \right)$$ The $$\mathcal{D}$$’s utility function in the $${\mathbb{G}}_{\mathcal{W}}^{\mathfrak{B}}$$ game
$${\mathcal{U}}_{\mathcal{D}}^{BES}\left(\cdot \right)$$ The $$\mathcal{D}$$’s utility function of BES in the $${\mathbb{G}}_{\mathcal{W}}$$
$${\mathcal{U}}_{\mathcal{D}}^{QPS}\left(\cdot \right)$$ The $$\mathcal{D}$$’s utility function of QPS in the $${\mathbb{G}}_{\mathcal{W}}$$
$${\mathbb{Q}}_{\mathfrak{B}}$$ All IoT devices, which generate QPSs
$${\mathbb{Q}}_{\mathcal{W}}$$ The $$\mathcal{W}$$’s IoT devices generated QPSs
$${\mathbb{W}}$$ The set of WiFi access points
$${\mathcal{W}}_{1\le i\le m}$$ The ith WiFi access point