p[3cm]{} |]{} & &\
$g_{21} = 1$ & $u_{1}(g_{12} = 1, g_{21} = 1),$ $u_{2}(g_{12} = 1, g_{21} = 1)$ & $u_{1}(g_{12} = 0, g_{21} = 1),$ $u_{2}(g_{12} = 0, g_{21} = 1)$\
$g_{21} = 0$ & $u_{1}(g_{12} = 1, g_{21} = 0),$ $u_{2}(g_{12} = 1, g_{21} = 1)$ & $u_{1}(g_{12} = 0, g_{21} = 0),$ $u_{2}(g_{12} = 0, g_{21} = 0)$\

Fig. \[figM1\] depicts the entropic region $\Gamma_{2}^{*}$ of the two random variables $X_{1}$ and $X_{2}$. The entropic region $\Gamma_{2}^{*}$ can be easily constructed by applying the three Shannon inequalities $H(X_{1})\leq H(X_{1},X_{2})$, $H(X_{2})\leq H(X_{1},X_{2})$, and $H(X_{1})+H(X_{2})\geq H(X_{1},X_{2})$. The intersection of these three hyperplanes in $\mathbb{R}_{+}^{3}$ results in the polyhedral cone depicted in Fig. \[figM1\]. The distance between an entropic vector (depicted by a thick dot inside $\Gamma_{2}^{*}$) and the corresponding entropic vector on $\tilde{\mathcal{H}}$ the light-colored hyperplane) with the same $H(X_{1})$ and $H(X_{2})$ is equal to the KL divergence. If $\mbox{KL}(X_{1},X_{2})=0$, then the entropic vector lies on $\tilde{\mathcal{H}}$, and the 2 agents have non-redundant information.

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