Additivity of a cooperative-game value ($\psi (v+w)=\psi (v)+\psi (w)$)

A value has cooperative-game additivity when adding two characteristic functions on the same player set adds their allocation vectors. Here $(v+w)(S)=v(S)+w(S)$ for every coalition. The sum of two simple cooperative games need not be simple; the axiom is naturally stated on transferable utility games.