 Convex cooperative game

A transferable utility game is convex when its coalition-value function is supermodular. Equivalently a player's marginal contribution cannot decrease when the preceding coalition grows. The implication follows by applying the displayed inequality to $A\cup \{i\}$ and $B$ with $A\subseteq B$, $i\notin B$; the reverse implication follows by adding successive marginal inequalities. This property concerns coalition values, not geometrical convexity of a strategy space.