On the non-compactness of the core of nonatomic convexσ-continuous measure games

Abstract

This paper concerns with the core of nonatomic games of form f(μ), whereμ is a nonatomic nonnegative measure and f is a continuous convex function on the domain ofμ. The main result of this paper is that the core of the game is not compact under the norm topology unless the game itself is a measure. This shows the largeness of the core in a sense other than that defined by Sharky for finite cases.