Nonemptiness of the Alpha‐Core

ABSTRACT We prove nonemptiness of the ‐core for balanced games with nonordered preferences, extending and generalizing in several aspects the results of Scarf (1971), Border (1984), Florenzano (1989), Yannelis (1991b), and Kajii (1992). In particular, we answer an open question in Kajii (1992) regarding the applicability of the nonemptiness results to models with infinite‐dimensional strategy spaces. We provide two models with Knightian and voting preferences for which the results of Scarf (1971) and Kajii (1992) cannot be applied, while our nonemptiness result applies.