Cores of Subconvex Games and Permutationally Convex Games

摘要

The core of cooperative games with side payments is studied. Three related properties of a cooperative game (convexity, subconvexity, and permutational convexity) which are sufficient for the nonemptiness of the core are examined. The existence of the core for subconvex and permutationally convex games is proved by specifying at least one extreme point of the core in terms of a stable marginal worth vector. Here a marginal worth vector is based on the marginal contributions of single players to coalitions of their predecessors with respect to a fixed ordering of the player set.