On restricted bargaining sets

In this paper we analyze the behavior of bargaining sets in continuum economies when there are restrictions on the formation of coalitions. We provide several characterizations of Vind's (J Math Econ 21:89-97, 1992) bargaining set in terms of its restricted versions, where not all the coalitions are formed. Moreover, we show that these equivalences do not hold for Mas-Colell's (J Math Econ 18:129-139, 1989) bargaining set. These findings highlight the different nature of both notions of bargaining sets. Finally, we illustrate the impossibility of extrapolating our results to a more general setting.