Marginal contribution vector ($m_i^{\pi }=v(P_i\cup \{i\})-v(P_i)$)

For a player ordering $\pi$, $P_i$ is the set before player $i$, and the displayed entries form its marginal contribution vector. Their sum is $v(N)-v(\varnothing )$. The Shapley value is the average of these vectors. In a convex cooperative game, increasing marginal contributions make each such vector satisfy every coalition constraint of the core of a cooperative game.