Uncertain discount and hyperbolic preferences

When the discount rate is uncertain, individuals whose preferences are consistent with discounted expected utility, exhibit diminishing impatience. This paper introduces and characterizes a variation of discounted expected utility in which the discount rate depends on the state of the nature that will occur. Quasi-hyperbolic discounting and the model of Dasgupta and Maskin (2005) are particular cases. The present bias disappears when the immediate payoff becomes uncertain. Commitment may be detrimental unless the discount rate is constant.