assume that the cost of forming a link between any two agents $i$ and $j$ is given by $c_{ij}=c,\forall\, i,j\in\mathcal{N}$. The goal of this section is to answer the following question: *given an entropic vector $\overrightarrow{{\bf H}}$, what are the network topologies $\mathcal{T}$ that can emerge at an NE of the game $\mathcal{G}^{N}$ when the link costs are homogeneous?* We start with the following motivating example to identify different factors that affect the equilibria of $\mathcal{G}^{2}$.

Motivating example for two-agents interaction: does information redundancy matter?
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Consider a simple network with only two agents ($N=2$) possessing random variables $X_{1}$ and $X_{2}$. We aim at characterizing the equilibria of $\mathcal{G}^{2}=\langle\{1,2\},{\bf G},{\bf u},\overrightarrow{{\bf H}}\rangle$. The strategy of agent 1 is simply a linking decision $g_{12}\in\{0,1\}$, while for agent 2, the strategy is $g_{21}\in\{0,1\}$. We write $\mathcal{G}^{2}$ in normal form in Table \[tab:title\], where the row player is agent 2 and the column player is agent 1. Each cell displays the utilities of agents 1 and 2 respectively. Assume that the link cost is the same for both agents and equal to $c$. It can be easily shown that the payoffs of agent 1 are given by $u_{1}(g_{12}=1,g_{21}=1)=u_{1}(g_{12}=1,g_{21}=0)=f\left(H(X_{1},X_{2})\right)-c$, $u_{1}(g_{12}=0,g_{21}=1)=f\left(H(X_{1},X_{2})\right)$, and $u_{1}(g_{12}=0,g_{21}=0)=f\left(H(X_{1})\right)$.

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