We study the interplay of probabilistic sophistication, second order stochastic dominance, and uncertainty aversion, three fundamental notions in choice under uncertainty. In particular, our main result, Theorem 2, characterizes uncertainty averse preferences that satisfy second order stochastic...

We study unique and globally attracting solutions of a general nonlinear equation that has as special cases some recursive equations widely used in Economics.

We study the equivalence between the MB-set and the core in the general context of games with a measurable space of players. In the first part of the paper, we study the problem without imposing any restriction on the class of games we consider. In the second part, we apply our findings to...

We study the cores of non-atomic market games, a class of transferable utility co- operative games introduced by Aumann and Shapley [2], and, more in general, of those games that admit a na-continuous and concave extension to the set of ideal coalitions, studied by Einy, Moreno, and Shitovitz...

A definition of set-wise differentiability for set functions is given through refining the partitions of sets. Such a construction is closely related to the one proposed by Rosenmuller (1977) as well as that studied by Epstein (1999) and Epstein and Marinacci (2001). We present several classes...

Concavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members are concave whenever they are supermodular. We show that for some important Riesz spaces both the...

We introduce a notion of complete monotone quasiconcave duality and we show that it holds for important classes of quasiconcave functions.

We study uncertainty averse preferences, that is, complete and transitive preferences that are convex and monotone. We establish a representation result, which is at same time general and rich in structure. Many objective functions commonly used in applications are special cases of this...

We consider a game, called newsvendor game, where several retailers, who face a random demand, can pool their resources and build a centralized inventory that stocks a single item on their behalf. Profits have to be allocated in a way that is advantageous to all the retailers. A game in...

When there is uncertainty about interest rates (typically due to either illiquidity or defaultability of zero coupon bonds) the cash- additivity assumption on risk measures becomes problematic. When this assumption is weakened, to cash-subadditivity for example, the equivalence between convexity...