Nested/Recursive Dynastic Utility Functions
Here are two nice papers on recursive utility functions, a generalization of additive utility functions and compatible with &quot;utility of the dynastic head to be partly a function of the utility of his children and grandchildren's utility, but where his children's utility is again partly a function of his grandchildren's and great-grandchildren's utility, and so on&quot;:
Blackorby, C., Nissen, D., Primont, D., &amp; Russell, R. (1973). Consistent Intertemporal Decision Making. The Review of Economic Studies, 40(2), 239-248.
Blackorby, C., Nissen, D., Primont, D., &amp; Russell, R. (1974). Recursively Decentralized Decision Making. Econometrica, 42(3), 487-496.