\[supsupadlll\] will be satisfied for every $ 0 \leq \gamma_{i}, \gamma_{j} \leq 1 $. Specifically, the underlying reason for being a superaddition in the *selfish-selfish* coalition of $ \gamma_{i}= \gamma_{j}= 1 $ is that it will increase the collective efficiency only due to the use of random information that two players share with each other.

Secondly, in the case of a *sacrifice-sacrifice* coalition, $ \gamma_i = (\gamma_i , 0 ) \,\, \& \,\, \gamma_j = (\gamma_j , 0 ) $, we can obtain $ r_{max}^i  = p ( \gamma_i ) $, $ r_{max}^j  = p ( \gamma_j ) $ according to Eq. \[eqrmaxx\] that is independent of $ \alpha_{i} \,\, \& \,\, \alpha_{j} $. Therefore, $$r_{col-PO} ( \alpha_{i}, \alpha_{j}, \gamma_{1i} = \gamma_i , \gamma_{2j}= 0 ) = r_{col-FO} (\gamma_{i}, \gamma_{j} ).
\label{adlkntkacx}$$ Hence, every *sacrifice-sacrifice* coalition will be an additive game.

On the contrary, while there are a plenty of selections which for them the coalition is superadditive, especially in the big $ \alpha $ factors (see Fig. \[colcoclckeh1\] for $\alpha_{i} = \alpha_{j} =1$), there are a variety of other selections for which, $ r_{col-PO} < r_{col-FO} $, according to the example of Fig. \[colclckeh0\], especially for small observability parameters.

