We consider <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$H$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>H</mi> </math> </EquationSource> </InlineEquation> expected utility maximizers that have to share a risky aggregate multivariate endowment <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$X\in {\mathbb {R}}^{N}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>X</mi> <mo>∈</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </mrow> </math> </EquationSource> </InlineEquation> and address the following two questions: does efficient risk-sharing imply restrictions on the form of individual consumptions as a...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

Consider a group consisting of S members facing a common budget constraint p'xi=1: any demand vector belonging to the budget set can be (privately or publicly) consumed by the members. Although the intragroup decision process is not known, it is assumed to generate Pareto-efficient outcomes;...