We study two alternative definitions of the bargaining set in large (a
tomless) economies; the local bargaining by MasColell (1989) and the g
lobal bargaining set by Vind (1992). We alter these definitions to lim
it the size of the permitted size of the involved coalitions. It turns
out that the local bargaining set becomes very large, whereas the glo
bal bargaining set is unaltered.