The Nash solution is more utilitarian than egalitarian

I state and prove formal versions of the claim that the Nash (Econometrica 18: 155–162, 1950) bargaining solution creates a compromise between egalitarianism and utilitarianism, but that this compromise is “biased”: the Nash solution puts more emphasis on utilitarianism than it puts on egalitarianism. I also extend the bargaining model by assuming that utility can be transferred between the players at some cost (the transferable and non-transferable utility models are polar cases of this more general one, corresponding to the cases where the transfer cost is zero and infinity, respectively); I use the extended model to better understand the connections between egalitarianism and utilitarianism.