–cycle; | (1.52,2.2,1.2)–(2.25,2.2,-0.5); at (3.25,2.2,-0.5) [$\mbox{KL}(X_{1},X_{2})$]{}; at (-0.5,2.5,2.5) [$\Gamma_{2}^{*}$]{}; (-0.5,0.5,2.5) node\[ann\] [$H(X_{1})$]{} (0.5,3,0.5) node\[ann\] [$H(X_{1},X_{2})$]{} (3,0.5,0.5) node\[ann\] [$H(X_{2})$]{};

(0,0,0)–(0,3.5,3.5); (0,0,0)–(2,2,0); (2.5,3.5,2.5)–(3,4.25,2.5);

The equilibria of this game depend on both the link cost and the entropic vector, which corresponds to the amount of information redundancy. For an arbitrary entropic vector, the game has two possible equilibria ${\bf g}^{*}=(g_{12}=1,g_{21}=0)$ and ${\bf g}^{*}=(g_{12}=0,g_{21}=1)$ if $c\leq f(H(X_{1},X_{2}))-f\left(\max\{H(X_{1}),H(X_{2})\}\right)$. Assume that $H(X_{1})>H(X_{2})$. Therefore, the network has a unique equilibrium ${\bf g}^{*}=(g_{12}=0,g_{21}=1)$ when $f(H(X_{1},X_{2}))-f(H(X_{1}))\leq c\leq f(H(X_{1},X_{2}))-f(H(X_{2}))$, and a unique equilibrium ${\bf g}^{*}=(g_{12}=0,g_{21}=0)$ when $c\geq f(H(X_{1},X_{2}))-f(H(X_{2}))$. On the other hand, if we fix the link cost and the entropies $H(X_{1})$ and $H(X_{2})$, we observe that the equilibria change by changing the KL divergence. For instance, the network has two equilibria ${\bf g}^{*}=(g_{12}=1,g_{21}=0)$ and ${\bf g}^{*}=(g_{12}=0,g_{21}=1)$ when $c\leq f(H(X_{1})+H(X_{2})-\mbox{KL}(\mathcal{X}))-f\left(\max\{H(X_{1}),H(X_{2})\}\right)$. Thus, as the entropic vector becomes closer to the hyperplane $\tilde{\mathcal{H}}$, i.e. $\mbox{KL}(\mathcal{X})$ decreases, the cost threshold for which these two equilibria emerge increases. This means that the characterization of the NE is sensitive to the amount of information redundancy $\mbox{KL}(\mathcal{X})$, even if we fix the individual entropies $H(X_{1})$ and $H(X_{2})$. Note that the strategy profile ${\bf g}=(g_{12}=1,g_{21}=1)$ never emerges as an NE since under such profile any of the 