The Nash bargaining solution for decision weight utility functions

A simple derivation of the non-expected utility Nash outcome, as defined in Rubinstein et al. (1992) [Rubinstein, A., Safra, Z., Thomson, W., 1992. On the interpretation of the Nash bargaining solution and its extension to non-expected utility preferences. Econometrica, 60, 1171–1186] is given for the class of decision weight utility functions. Conditions for existence and uniqueness are provided.