Stability and Largeness of the Core

In general, there are examples of TU games where the core is stable but is not large. In this paper, we show that the extendability condition introduced by Kikuta and Shapley (1986, “Core Stability in n-Person Games,” Mimeo) is sufficient for the core to be stable as well as large, for TU games with five or fewer players. We provide a counter example when the number of players is six. We then introduce a stronger extendability condition and show that it is necessary and sufficient for the core to be large. Our proof makes use of a well-known result from the theory of convex sets. Journal of Economic Literature Classification Number: C71.