Reconciling the Nash and Kalai-Smorodinsky Cooperative Solutions: Generalized Maximands of CES Form

This note suggests variations to the baseline Nash cooperative solution that take into account the Kalai-Smorodinsky critique. One the one hand, a CES form of the maximand is proven to accommodate both the generalized two-person Nash and the Kalai-Smorodinsky - as other proportional - solutions as special cases. As an alternative, a Stone-Geary formulation is forwarded, weighing both the distances to the threat and to the ideal point, along with the corresponding CES generalization. Interpretations of the implied equilibrium solutions – generalizable to n-person cooperative games – are provided, arising as equations balancing geometric averages of measures of attitude towards (large) risk(s) of the players.