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...

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>

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...

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...

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...

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...

In repeated games with public monitoring, the consideration of behavior strategies makes relevant the distinction between public and private strategies. Recently, Kandori and Obara [6] and Mailath, Matthews and Sekiguchi [8] have provided examples of games with equilibrium payoffs in private...

The paper provides a notion of measurability which is suited for a class of Multiple Prior Models. Those characterized by nonatomic countably additive priors. Preferences generating such representations have been recently axiomatized in [12]. A notable feature of our definition of measurability...

The paper provides a notion of measurability for Multiple Prior Models characterized by nonatomic countably additive priors. A notable feature of our definition of measurability is that an event is measurable if and only if it is unambiguous in the sense of Ghirardato, Maccheroni and Marinacci...