I state and prove formal versions of the claim that the Nash 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 ; I use the extended model to better understand the connections between egalitarianism and utilitarianism.