We study the cores of non-atomic market games, a class of transferable utility cooperative 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...

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...

For (S, S) a measurable space, let C1 and C2 and be convex, weak* closed sets of probability measures on S. We show that if C1 C2 satisfies the Lyapunov property, then there exists a set A S such that min C1 (A) max C2 (A). We give applications to Maxmin Expected Utility and to the core of a...

For (S, Σ) a measurable space, let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\cal C}_1$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\cal C}_2$$</EquationSource> </InlineEquation> be convex, weak<Superscript>*</Superscript> closed sets of probability measures on Σ. We show that if <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${\cal C}_1$$</EquationSource> </InlineEquation> ∪ <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${\cal C}_2$$</EquationSource> </InlineEquation> satisfies the Lyapunov property , then there exists a set A ∈ Σ such that min<Subscript>μ1</Subscript>∈<InlineEquation ID="IEq5"> <EquationSource...</equationsource></inlineequation></subscript></equationsource></inlineequation></equationsource></inlineequation></superscript></equationsource></inlineequation></equationsource></inlineequation>

Existential and constructive solutions to the classic problems of fair division are known for individuals with constant marginal evaluations. By considering nonatomic concave capacities instead of nonatomic probability measures, we extend some of these results to the case of individuals with...

The concept of Ambiguity designates those situations where the information available to the decision maker is insufficient to form a probabilistic view of the world. Thus, it has provided the motivation for departing from the Subjective Expected Utility (SEU) paradigm. Yet, the formalization of...

We provide a representation theorem for risk measures satisfying (i) monotonicity; (ii) positive homogeneity; and (iii) translation invariance. As a simple corollary to our theorem, we obtain the usual representation of coherent risk measures (i.e., risk measures that are, in addition,...

Continuous exact non-atomic games are naturally associated to certain operators between Banach spaces. It thus makes sense to study games by means of the corresponding operators. We characterize non-atomic exact market games in terms of the properties of the associated operators. We also prove a...

We provide a representation theorem for risk measures satisfying (i) monotonicity; (ii) positive homogeneity; and (iii) translation invariance. As a simple corollary to our theorem, we obtain the usual representation of coherent risk measures (i.e., risk measures that are, in addition,...