- \frac{q ( \gamma_{I} )}{p ( \gamma_{pa} ) } . q ( \gamma_{I} ) \right] \right\rbrace .
\label{lalbkusab}$$ Remembering the efficiency of a given agent in a fully observable environment, $ r_{FO} = p ( \gamma_{pa} ) $, then $$r_{PO} = \beta \,\, r_{FO} , \qquad 0 \leq \beta \leq 1 \quad \Longrightarrow \quad  r_{PO} \leq r_{FO}.$$ We may recall $ \beta $ as a transparency coefficient or $ \mu = 1 - \beta $ as the reduction of transparency. Besides, one can have $ q $ with respect to $ p $ according to the specific form of $ h $-matrix within a given problem, see Eq. \[diwwonehhha\] for instance, for which $$If \quad p + q \, ( N-1 ) = 1,$$ $$\mu = (1 - \alpha ) \, q ( \gamma_{I} ) \left[ (N - 1) - \frac{q ( \gamma_{pa} )}{p ( \gamma_{pa} ) } \right]  , \quad N \geq 2.$$\
Our formulation can go beyond to include multi-agent games where an interpreter could be a sort of protagonist agent by itself and a protagonist agent, on the other hand, would be an intelligent interpreter too so that every agent become a simultaneous player-interpreter (see Sec. \[sectionmmultii\]). 