Diversification, Convex Preferences and Non-Empty Core
We show, in the Choquet expected utility model, that prefernece for diversification, that is, convex prefrences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversification, namely "sure diversification". We show that this implies that the core of the capacity be non-empty. The converse hodls under concavity of the utility index.
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