A necessary condition for the coincidence of the bargaining sets dened by Shimomura (1997) and the core of a cooperative game with transferable utility is provided. To this aim, a set of payo vectors, called max-payo vectors, are introduced. This necessary condition simply checks whether these...

The Böhm-Bawerk horse markets are assignment markets with homogeneous goods that are known to have a one-dimensional core. We show here that, although there exist two-sided assignment games with non-homogeneous products and with a segment as a core, the Böhm-Bawerk horse markets are the only...