Patience in some non-additive models

Our aim is to give an axiomatization of preferences over infinite consumption streams. At first we adopt the additive case, and give a characterization of preferences which satisfy patience [Marinacci, M., 1998. An axiomatic approach to complete patience and time invariance. Journal of Economic Theory 83, 105–144] or equivalently what Diamond [Diamond, P.A., 1965. The evaluation of infinite utility streams. Econometrica 33, 170–177] named equal treatment of all generations and then, focus on stationary additive preferences. It appears that this class of functionals contains the discounting functionals axiomatized in Koopmans [Koopmans, T.C., 1972. In: McGuire, C.B., Radner, R. (Eds.), Representations of Preference Orderings Over Time. Decision and Organization, North-Holland, Amsterdam] and what is known as Banach-Mazur limit functionals. These results are extended to non-additives preferences where similar results are generalized and naive patience receives a positive treatement through the liminf criterion.