CONVEX COVERS OF SYMMETRICAL GAMES

We consider a multi-player, cooperative, transferable-utility, symmetr ic game (N, v) and associated convex covers, i.e., convex games (N, (v ) over tilde) such that (v) over tilde greater than or equal to v. A c onvex cover is efficient iff (v) over tilde(empty set) = v(empty set) and (v) over tilde(N) = v(N); and minimal iff there is no convex cover (v) over tilde not equal (v) over tilde such that (v) over tilde less than or equal to (v) over tilde. Efficient and minimal convex covers are closely related to the core of(N, v); in fact, extreme points of t he core are shown to correspond to efficient convex covers which are m inimal and extreme. A necessary and sufficient condition is provided f or minimality, and another for extremity. Construction of convex cover s and a form of decomposition are treated in derail, and some useful p roperties are identified which may be recognized in terms of visibilit y of points on a graph of(N, v) and other elementary concepts.