On the core and bargaining set of a veto game

The notion of veto player was originally introduced in simple games (see Nakamura in Int J Game Theory 8:55-61, 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 (and other solution concepts) for these "veto games". In particular, for this class of games, we show the equivalence between the core and the bargaining set. Our work generalizes the clan games and big-boss games introduced respectively by Potters et al. (Games Econ Behav 1:275-293, 1989) and Muto et al. (Econ Stud Q 39:303-321, 1988).