assume that the agents benefit from acquiring information increases, while the marginal benefit decreases, with the increase of the amount of information gathered. That is, in a sensor network setting, the benefit of a sensor node from collecting information saturates if it is connected to a large number of sensors; thus, $f(.)$ is assumed to be twice continuously differentiable, increasing, and concave with $f(0)=0$. Note that the total information acquired by $i$ in (\[eq02\]) can be written in terms of the conditional entropies based on the chain rule as [@ref21] $$H(X_{i\cup\mathcal{R}_{i}({\bf g})})=H(X_{i})+\sum_{k=1}^{|\mathcal{R}_{i}({\bf g})|}H(X_{j_{k}}|X_{i},\left\{X_{j_{m}}\right\}_{m=1}^{k-1}),$$ where $\mathcal{R}_{i}({\bf g})=\{j_{1},j_{2},...,j_{|\mathcal{R}_{i}({\bf g})|}\}$, which implies that agents benefit by acquiring new information conditioned on its own information and the information it acquires from other connections. Moreover, the aggregate information can be expressed in terms of the mutual information as $$H(X_{i\cup\mathcal{R}_{i}({\bf g})})=H(X_{i})+H(X_{\mathcal{R}_{i}({\bf g})})-I(X_{i};X_{\mathcal{R}_{i}({\bf g})}),$$ where the term $H(X_{\mathcal{R}_{i}({\bf g})})$ represents the net information that agent $i$ acquires after connecting to the agents in $\mathcal{N}_{i}({\bf g})$, where the term $I(X_{i};X_{\mathcal{R}_{i}({\bf g})})$ captures the redundancy between the information of agent $i$ and the information it acquires from the set $\mathcal{R}_{i}({\bf g})$. Let ${\bf u}=(u_{1},u_{2},...,u_{N})$. Throughout the paper, we denote the network formation game by $\mathcal{G}^{N}\langle\mathcal{N},{\bf G},{\bf u},\overrightarrow{{\bf H}}\rangle$. We 