On the equivalency of balancedness and stability in effectivity function games

In this paper the authors first introduce effectivity functions and some of their properties, especially balancedness. By using a specific characteristic function which enables us to transform a game in the effectivity function form into that of the characteristic function form, the authors show that balancedness of the effectivity functions is sufficient for the stability, i.e., the existence of the core whatever preference ordering each player has. The present main result states that balancedness is a necessary and sufficient condition for the stability as long as the effectivity functions satisfy anonymity and neutraility.