Core equivalence in coalition production economies

Equivalence between the core and the set of competitive allocations is shown to hold in the limit for large coalition production economies that allow for both decreasing returns to scale and superadditivity of the technology correspondence. Along the way, we shed some light on a separation argument problem with the alleged proof in Böhm (1974a), and on the unfortunate stringency—in terms of an implied near absolute degree of uniformity of ideas or production capabilities across society—of Arrow and Hahn’s (1971) assumptions to tackle core equivalence. Our approach both amends the existing proofs in the literature and widens the scope of the Core Equivalence Theorem, as we show not only by weakening its hypotheses but also by proposing an extension of this classic result to a fuzzy coalition production economy a la Aubin (1979).