An Investigation of Time Consistency for Subjective Discontinued Utility

A well-known common agreement in decision theory is that only exponential decision makers are time consistent i.e. with the mere passage of time, future choices must not contradict the initial choice. Building on this result, a large range of works has studied time inconsistency as a direct application of hyperbolic discounting. These articles share the common objective time assumption under which decision makers have a perfect perception of future periods. This paper firstly highlights that, when no further condition than separability is mentioned, any discount mechanism is compatible with time consistency. Then, we investigate time consistency assuming that individual time perception may be submitted to time distortion. In particular, an axiomatic discounting model called Subjective Discounted Utility (SDU) is provided to illustrate how hyperbolic decision makers may be time consistent.