## 3 System Model  
We consider the case where a single macrocell \(B\!S_{0}\) and a set of open access picocells \(\{B\!S_{i}\ |i\ =\ 1,...,M\}\) coexist and overlap with one another. We ignore the macrocells around this single macrocell, because ICI between heterogeneous cells obviously has a higher magnitude than ICI between homogeneous cells, so this simplification does not affect the results much. There are in total \(N_{0}\) densely-deployed sensor and mobile devices in the scenario, given by \(\mathbf{DV}_{All}=\{D\!V_{j}|j=1,...,N_{0}\}\). Note that the assumption of the dense deployment of the devices guarantees the rationality to evaluate the ICI on a given device by taking an average of all of the devices that interfere with it, as analyzed in Section 4.2 later. The cell radius of \(B\!S_{i}\) is denoted by \(R_{i}\), and the number of devices under the coverage of \(B\!S_{i}\) is given by \(N_{i}\). We assume that all of the devices are uniformly distributed within the disc coverage area of \(B\!S_{0}\), so the density of devices is given by \(\rho=N_{0}/\pi R_{0}^{2}\). \(N_{i}=N_{0}R_{i}^{2}/R_{0}^{2}\), \(\forall i\in\{1,...,M\}\). Main notations are summarized in Table 3. Without a specific description, notations follow the rule that, the subscript \(i=0\) represents the macrocell and \(i\in\{1,...,M\}\) represents the \(i\)-th picocell. Devices selecting \(B\!S_{i},i\in\{1,...,M\}\) are given by \(\mathbf{DV}_{i}\). Data can be transmitted directly between the BS and a device or indirectly through a coordinator (or relay). For indirect transmission through a coordinator, we assume that the link between the BS and the coordinator is wireless, so it is identical to the case when the coordinator itself transmits to the BS. Meanwhile, transmissions between sensors and their coordinators are on unlicensed frequency bands with extremely low transmission power, which do not cause ICI and do not even occupy resources in licensed bands. In a word, direct and indirect connections can be modeled identically for evaluating ICI in the CS game. We assume that all of the \begin{table}
\begin{tabular}{c l} \hline \(B\!S_{i}\) & BS of cell \(i\) \\ \hline \(\mathbf{DV}_{i}\) & Devices selecting \(B\!S_{i}\) \\ \hline \(\mathbf{DV}_{All}\) & All of the devices within the coverage of the macrocell disc area \\ \hline \(D\!V_{j}\) & The \(j\)-th device in a set of devices \\ \hline \(N_{i}\) & Number of devices within the coverage of cell \(i\) \\ \hline \(R_{i}\) & Radius of the disc area covered by \(B\!S_{i}\) \\ \hline \(P_{i}\) & Uplink transmission power of the devices to \(B\!S_{i}\) \\ \hline \(B_{i}\) & Total available bandwidth for cell \(i\) \\ \hline \(I_{ij}\) & Average ICI from the devices in cell \(B\!S_{i}\) to \(B\!S_{j}\) \\ \hline \(n_{i}\) & Number of devices selecting \(B\!S_{i}\) \\ \hline \(D_{ij}\) & Distance between \(B\!S_{i}\) and \(B\!S_{j}\) \\ \hline \(d_{ij}\) & Distance between \(B\!S_{i}\) and \(D\!V_{j}\) \\ \hline \(r_{i}\) & Radius of the disc area formed by the devices selecting cell \(i\) \\ \hline \(p_{j}\) & Pure strategy of \(D\!V_{j}\) \\ \hline \(U_{j}\) / \(C_{j}\) & Utility/cost function of \(D\!V_{j}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Main notations. devices are identical for their traffic type, terminal property and user preference, so it is reasonable to assume that \(\mathbf{DV}_{i}\) are the \(n_{i}\) devices closest to \(B\!S_{i}\), forming a disc area with radius \(r_{i}\), and \(n_{i}=N_{0}r_{i}^{2}/R_{0}^{2}\), as demonstrated by the azure circle in Figure 2. If the above features of various devices are not identical in reality, a function combining these features is used to represent the unified tendency for selecting each cell, which can be considered as a virtual distance when mapping into our system model.