LARGENESS OF THE CORE OF k-CONVEX SYMMETRIC GAMES

Abstract

A cooperative TU game is said to posses a large core as defined by Sharkey [1982] if for every acceptable vector there is a smaller core vector in the game. This paper is devoted to characterization(s) of largeness of the core of a subclass of games known as k-convex games (containing the convex games in case k = n). The k-convex games were defined by Driessen [1988] because of the core structure they possess, which is the same as that of a suitably defined convex game. The main goal is to show that the totally balanced symmetric k-convex games possess a large core if and only if the game is convex.