Extendable cooperative games

A (TU) cooperative game is extendable (Kikuta and Shapley, 1986) if every core allocation of each sub-game can be extended to a core allocation of the game. It is strongly extendable if any minimal vector in the upper core of any of its sub-games can be extended to a core allocation. We prove that strong extendability is equivalent to largeness of the core (Sharkey, 1982). Further, we characterize extendability in terms of an extension of the balanced cover of the game. It is also shown how this extension can unify the analysis of many families of games under one roof. JEL classification: C71