On the core and bargaining set of a veto game

The notion of veto player was originally introduced in simple games [see Nakamura (1979)], for which every coalition has a value of 0 or 1. In this paper we extend it to monotonic cooperative games with transferable utility: a player has veto power if all coalitions not containing her are worthless. We examine and characterize the core for each one of these "veto games". Moreover, we show the equivalence of the core and the bargaining set. Our work extends the clan games and big-boss games introduced respectively by Potters et al. (1989) and Muto et al. (1988).