We consider a multi-player, cooperative, transferable-utility, symmetric game (N, v) and associated convex covers, i.e. convex games (N, &vtilde;) such that &vtilde; ≥ v. A convex cover is efficient iff &vtilde;(Ø) = v(Ø) and &vtilde;(N) = v(N); and minimal iff there is no convex cover &vtilde; ≠ v; such that &vtilde; ≤ v. Efficient and minimal convex covers are closely related to the core of (N, v); in fact, extreme points of the core are shown to correspond to efficient convex covers which are minimal and extreme. A necessary and sufficient condition is provided for minimality, and another for extremity. Construction of convex covers and a form of decomposition are treated in detail, and some useful properties are identified which may be recognized in terms of visibility of points on a graph of (N,v) and other elementary concepts.
