An existence theorem for a bargaining set

Abstract This paper considers non-transferable utility games and provides sufficient conditions for the existence of the bargaining set introduced in Mas-Colell (1989). Our main assumption is weak balancedness. This assumption is weaker than balancedness and is satisfied in all transferable utility games and all three-player games. The proof of our main result is based on an application of a coincidence theorem of Fan (1969).