Limited arbitrage is necessary and sufficient for the non-emptiness of the core

A close connection is drawn between the non-emptiness of the core and limited arbitrage, a condition originally defined on the preferences and endowments of the traders of an Arrow-Debreu economy in Chichilnisky (1992, 1993b, 1994, 1995a,b). This condition limits the tradersʹ diversity, and bounds their mutually beneficial gains from trade