Convex Covers of Symmetric Games

John M. Rulnick and Lloyd Shapley
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John M. Rulnick: Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, USA

International Journal of Game Theory, 1998, vol. 26, issue 4, 577 pages

Abstract: We consider a multi-player, cooperative, transferable-utility, symmetric game (N, ) and associated convex covers, i.e., convex games (N, ~) such that ~ \geq . A convex cover is efficient iff ~(∅) = (∅) and ~(N) = (N); and minimal iff there is no convex cover ~ \neq ~ such that ~ \leq ~. Efficient and minimal convex covers are closely related to the core of (N, ); 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, ) and other elementary concepts.

Date: 1998-05-19
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