Empty-coalition normalization
= Empty-coalition normalization
{title2=$v(\varnothing)=0$}
The usual convention that the empty <coalition> creates no value. It makes the sum of a <marginal contribution vector> equal $v(N)$ by a <telescoping sum>. Without it, that sum is $v(N)-v(\varnothing)$, so the vector need not satisfy efficiency in the <core of a cooperative game>. The constant function $v(T)=1$ is <supermodular> but gives a zero marginal vector and fails efficiency for a nonempty player set.