A Mathematical Analysis of the Improving Sequence Effect for Monetary Rewards - Cruz Rambaud, Salvador; Muñoz Torrecillas, María José; Garcia, Adriana (Frontiers in Applied Mathematics and Statistics, 2018)
In this paper, we formalize mathematically the concept of improving sequence effect which is one of the main anomalies of the Discounted Utility model (Samuelson, 1937). The improving sequence effect implies a preference for a given sequence of outcomes which increase over time and has been empirically demonstrated for both monetary and non-monetary results (hedonic experiences and health-related outputs). Nevertheless, to the date, there is not a mathematical treatment of this anomaly in the context of intertemporal choice which allows us to relate this paradox to other anomalies, such as the delay and the magnitude effects. In this way, the present manuscript has filled this gap. More specifically, we have proved that the improving sequence effect for monetary rewards cannot be rationalized by using a separable discount function, but only considering a non-separable discount function. Moreover, under certain conditions, we have proved that the delay and the magnitude effects are necessary conditions for the existence of the improving sequence effect.