▁in ▁the ▁teams ▁and ▁their ▁reven ues , ▁as ▁illustrated ▁in ▁Figure ▁ 1 , ▁you ▁can ▁also ▁estimate ▁the ▁total ▁re venue ▁as ▁a ▁function ▁of ▁the ▁allocation . ▁This ▁is ▁exempl ified ▁in ▁Figure ▁ 2 ▁– ▁the ▁left - hand ▁side ▁of ▁the ▁graph ▁corresponds ▁to ▁alloc ating ▁all ▁resources ▁to ▁the ▁red ▁team , ▁while ▁the ▁right - hand ▁side ▁of ▁the ▁graph ▁corresponds ▁to ▁alloc ating ▁all ▁resources ▁to ▁the ▁blue ▁team . ▁A ▁simple ▁optimization ▁will ▁reve al ▁the ▁optimal ▁allocation ▁– ▁the ▁allocation ▁that , ▁under ▁your ▁estimate ▁of ▁the ▁re venue ▁functions , ▁will ▁yield ▁the ▁highest ▁re venue . ▁ ▁Int rodu cing ▁uncertainty ▁However , ▁this ▁analysis ▁does ▁not ▁take ▁uncertainty ▁into ▁account . ▁Since ▁the ▁re venue ▁functions ▁are ▁only ▁a ▁( poss ibly ▁rough ) ▁estimate , ▁the ▁actual ▁re venue ▁functions ▁may ▁be ▁quite ▁different . ▁For ▁any ▁level ▁of ▁uncertainty ▁( or ▁horizon ▁of ▁uncertainty ) ▁we ▁can ▁define ▁an ▁en velope ▁within ▁which ▁we ▁assume ▁the ▁actual ▁re venue ▁functions ▁are . ▁High er ▁uncertainty ▁would ▁correspond ▁to ▁a ▁more ▁inclus ive ▁en velope . ▁Two ▁of ▁these ▁uncertainty ▁en velop es , ▁surrounding ▁the ▁re venue ▁function ▁of ▁the ▁red ▁team , ▁are ▁represented ▁in ▁Figure ▁ 3 . ▁As ▁illustrated ▁in ▁Figure ▁ 4 , ▁the ▁actual ▁re venue ▁function ▁may ▁be ▁any ▁function ▁within ▁a ▁given ▁uncertainty ▁en velope . ▁Of ▁course , ▁some ▁instances ▁of ▁the ▁re venue ▁functions ▁are ▁only ▁possible ▁when ▁the