Consistent Intertemporal Decision-Making under Uncertainty

Abstract

Strotz [6] seems to have been the first to provide a formal analysis of the problem of inconsistency in intertemporal decision-making. An individual who plans for the future may find that as time elapses he wishes to revise his plan. Strotz examined the form of the discount function as a possible source of inconsistency, when there was no uncertainty facing the individual. His conclusions have subsequently been refined in work by Pollak [4], Heal [3] and Burness [1]. Hammond [2] has examined the problem in a more general context, and it is essentially his framework I use in what follows to characterize consistent planning under uncertainty. I prove that under certain assumptions, consistency is equivalent to maximizing expected utility on the set of feasible plans, with a restricted set of utility functions and a tree of subjective probability distributions which satisfy the Bayesian updating rule.