An Alpha-Maxmin Axiomatisation of Temporally-Biased Multiple Discounts

This article studies an axiomatic approach of inter-temporal utility streams that takes into account evaluations of stream's close future and distant future. A detailed characterization of sets of discount rates systems used to evaluate the close and distant future is presented. This is followed by a generalization of quasi-hyperbolic discounting in the context of close future evaluation. A similar analysis for the distant future is also performed. It is proven that Banach limits, in the evaluation of the distant future, can be considered a counterpart of exponential discounting in the evaluation of the close future. The whole result can be given in an $\alpha$-MaxMin representation