Empty-coalition normalization ($v(\varnothing )=0$)

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.