Super-modularity: Applications to convex games and to the greedy algorithm for LP

L. S. Shapley (Internat. J. Game Theory1 (1971), 11–26) showed that if a game is convex, then all the marginal worth vectors are members of the core. J. Edmonds (in “Combinatorial Structures and Their Applications” (R. Guy et al., Eds.), pp. 69–87, Gordon & Breach, New York, 1970) considered a class of linear programming problems for which the greedy algorithm works. The present paper unifies these studies, and establishes the converse of each theorem.