 Superadditivity and nonempty core do not imply Shapley stability

On three players, let $v(S)=1$ exactly when $S$ contains player 1 and at least one of players 2 and 3, and zero otherwise. This simple cooperative game is superadditive: disjoint coalitions cannot both contain player 1, so at most one can have value one. Its core of a cooperative game is exactly $\{(1,0,0)\}$, since singleton nonnegativity and the two winning-pair constraints force the other two coordinates to zero. In a random player ordering, player 1 is pivotal unless it comes first, whereas each other player is pivotal in just one of the six orders. Thus its Shapley value is $(2/3,1/6,1/6)$, outside the core: coalition $\{1,2\}$ receives only $5/6<1$. Convex cooperative games have the stronger property that their Shapley value belongs to the core of a convex game.