Nash (1950) considered a domain of convex bargaining problems. We analyse domains including, or even consisting of, finite problems and provide various characterisations of the Nash Bargaining Solution (NBS). In particular, we extend Kaneko's (1980) results.

The Nash Bargaining Solution is characterised by using the new axiom of Maximal Symmetry in place of Nash's Independence of Irrelevant Alternatives and Symmetry. This axiom expresses the idea that a fair arbitrator should treat symmetric alternatives in the same way, subject to the feasibility...