G-continuity, impatience and myopia for Choquet multi-period utilities

A main goal of this paper is to try to clarify the notions of impatience and myopia, often considered as synonymous in the literature. The occurrence of asset price bubbles (see Araujo et al., 2011) when only myopia is required, explains why we focused on a stronger notion that we define as impatience and which allows to avoid such market anomalies. The first part characterizes the impatience and the myopia in the context of discrete and continuous time flows of income (consumption) valued through a Choquet integral with respect to an (exact) capacity. Our results unlike the additive utility functional allow to disentangle myopia from impatience: impatience requires myopia but the converse is false. Moreover it turns out that in our framework a decision maker exhibits more easily impatience and myopia in continuous time than in discrete time. In the second part, we recall the generalization given by Rébillé (2008) of the Yosida-Hewitt decomposition of an additive set function into a continuous part and a pathological part and use it to give a characterization of those convex capacities whose core contains at least one G-continuous measure. We then proceed to characterize the exact capacities whose core contains only G-continuous measures thus connecting some previous characterizations of impatience and myopia with core properties of exact capacities. As a dividend, a simple characterization of countably additive Borel probabilities on locally compact σ-compact metric spaces is obtained.