hand, agents in the $\mathcal{K}_{M}$ region can end up gathering different amounts of information as there are potentially multiple equilibria with different topologies and connectedness. In the following illustrative example, we demonstrate the impact of the link cost and information redundancy on the network’s connectivity regions.

To illustrate the impact of information redundancy and link cost on the NE networks’ connectivity, we plot the $\mathcal{K}_{M}$, $\mathcal{K}_{C}$, and $\mathcal{K}_{I}$ regions in the link cost-information redundancy plane for 2 different families of entropic vectors. Assume that we have a 3-agent CIN, with $H(X_{1})>H(X_{2})$, and $H(X_{2})=H(X_{3})$, and that agent 1 has non-redundant information, i.e. the random variable $X_{1}$ is independent on $X_{2}$ and $X_{3}$. Thus, we have $\mbox{KL}(\mathcal{X})=I(X_{2};X_{3})$. We consider two different families of entropic vectors (i.e. two different assignments for the values of individual agents’ entropies), the first is given by $(H^{1}(X_{1}) = 5, H^{1}(X_{2}) = 4, H^{1}(X_{3}) = 4)$, whereas the second is given by $(H^{2}(X_{1}) = 7, H^{2}(X_{2}) = 4, H^{2}(X_{3}) = 2)$. The connectivity regions associated with entropic vector family $i$ is denoted by $\left(\mathcal{K}_{C}^{i},\mathcal{K}_{I}^{i},\mathcal{K}_{M}^{i}\right)$. An exemplary utility function of $f(x)=\log(1+x)$ is used. In Fig. 2, we plot the connectivity regions in the cost-KL divergence plane for the 2 