▁of ▁no ▁subs id y , ▁introdu cing ▁a ▁small ▁subs id y ▁can ▁improve ▁a ▁country ' s ▁w elf are . ▁ ▁Ext ended ▁government ▁game ▁The ▁basic ▁model ▁can ▁be ▁extended ▁to ▁incorpor ate ▁a ▁sup ra - game ▁played ▁by ▁the ▁govern ments ▁of ▁the ▁respective ▁countries . ▁In ▁this ▁case , ▁each ▁government ▁cho oses ▁the ▁level ▁of ▁subs id y ▁it ▁will ▁provide ▁to ▁its ▁firm , ▁taking ▁the ▁other ▁government ' s ▁action ▁as ▁given , ▁and ▁anticip ating ▁the ▁reaction ▁of ▁the ▁fir ms ▁( in ▁terms ▁of ▁quantity ▁produced ) ▁to ▁the ▁subs id y . ▁Br ander ▁and ▁Sp encer ▁show ▁that ▁in ▁the ▁resulting ▁Nash ▁equilibrium ▁the ▁govern ments ▁choose ▁a ▁level ▁of ▁subs id y ▁that ▁is ▁too ▁high ▁and ▁hence ▁they ▁do ▁not ▁manage ▁to ▁maxim ize ▁social ▁w elf are . ▁In ▁fact , ▁if ▁the ▁good ▁produced ▁is ▁not ▁consum ed ▁dom est ically , ▁then ▁the ▁optimal ▁level ▁of ▁subs id y ▁is ▁negative ▁– ▁an ▁export ▁tax . ▁This ▁is ▁because ▁the ▁total ▁quantity ▁produced ▁in ▁the ▁Cour not ▁and ▁the ▁Stack el berg ▁equilibrium ▁is ▁higher ▁than ▁the ▁profit ▁maxim izing ▁coll us ive ▁mon opol y ▁level ▁of ▁output . ▁Since ▁both ▁the ▁home ▁and ▁foreign ▁firm ▁are ▁producing ▁for ▁a ▁third ▁market , ▁an ▁export ▁tax ▁could ▁reduce ▁the ▁total ▁quantity ▁produced ▁down ▁to ▁the ▁mon opol y ▁level , ▁thus ▁increasing ▁both ▁fir ms ' ▁prof its . ▁In ▁that ▁way ▁the