▁a ▁sympath etic ▁Nature ▁will ▁aim ▁to ▁select ▁a ▁state ▁that ▁will ▁satisfy ▁the ▁constraint . ▁As ▁for ▁the ▁outcome , ▁the ▁penalty ▁for ▁viol ating ▁the ▁constraint ▁is ▁such ▁that ▁the ▁decision ▁mak er ▁will ▁ref rain ▁from ▁selecting ▁a ▁decision ▁that ▁will ▁allow ▁Nature ▁to ▁viol ate ▁the ▁constraint ▁within ▁the ▁state ▁space ▁per tain ing ▁to ▁the ▁selected ▁decision . ▁ ▁The ▁role ▁of ▁" min " ▁and ▁" max " ▁▁ ▁It ▁should ▁be ▁str essed ▁that ▁the ▁feature ▁according ▁info - g ap ' s ▁robust ness ▁model ▁its ▁typical ▁Max imin ▁character ▁is ▁not ▁the ▁presence ▁of ▁both ▁ ▁and ▁ ▁in ▁the ▁form ulation ▁of ▁the ▁info - g ap ▁model . ▁R ather , ▁the ▁reason ▁for ▁this ▁is ▁a ▁deeper ▁one . ▁ ▁It ▁goes ▁to ▁the ▁heart ▁of ▁the ▁concept ual ▁framework ▁that ▁the ▁Max imin ▁model ▁capt ures : ▁Nature ▁playing ▁against ▁the ▁DM . ▁ ▁This ▁is ▁what ▁is ▁cru cial ▁here . ▁ ▁To ▁see ▁that ▁this ▁is ▁so , ▁let ▁us ▁general ize ▁info - g ap ' s ▁robust ness ▁model ▁and ▁consider ▁the ▁following ▁modified ▁model ▁instead : ▁ ▁where ▁in ▁this ▁context ▁ ▁is ▁some ▁set ▁and ▁ ▁is ▁some ▁function ▁on ▁. ▁Note ▁that ▁it ▁is ▁not ▁assumed ▁that ▁ ▁is ▁a ▁real - valu ed ▁function . ▁ ▁Also ▁note ▁that ▁" min " ▁is ▁absent ▁from ▁this ▁model . ▁ ▁All ▁we ▁need ▁to ▁do ▁to ▁incorpor ate ▁a ▁min   ▁into ▁this