Some infinite-player generalizations of Scarf's theorem: Finite-coalition alpha-cores and weak alpha-cores

摘要

In this paper, we first obtain some infinite-dimension versions of Scarf's theorem. Second, we provide two generalizations of Scarf (1971) to normal-form games with infinitely many players. Under the assumptions analogous to Scarf (1971), we prove the nonemptiness of the finite-coalition alpha-core. Furthermore, by strengthening the assumptions, we obtain the nonemptiness of the weak alpha-core, and show that the weak alpha-core coincides with the closed-coalition alpha-core. (C) 2017 Elsevier B.V. All rights reserved.