Dual coalitional game
= Dual coalitional game
{title2=$v'(S)=v(N)-v(N\setminus S)$}
Duality assigns a <coalition> the grand-coalition value less the value of its complement. For a normalized <transferable utility game>, the dual is normalized and taking the dual twice recovers the original game. A player's dual <marginal contribution> at predecessor set $S$ equals its original contribution at the complementary predecessor set in $N\setminus\{i\}$. This preserves the <Shapley value>.