Existence of the core in a heterogeneous divisible commodity exchange economy
The author considers a pure exchange economy of a heterogeneous divisible commodity modelled as a measurable space \((X, \Sigma)\). There are \(n\) persons having shares \(B_i\) (\(i=1,\dots,n\)) of \(X\), and the shares are valued according to individuals' finite vector measures \(\mu_i\). The components of vectors \(\mu_i(B_i)\) are measures of different attributes of \(B_i\). Individual \(i\) has a preference \(\succ_i\) over his profiles \(\mu_i(B)\), \(B\in\Sigma\). The existence of a weak core in the corresponding \(n\)-persons game is proved under assumption of rationality, continuity and convexity of the preferences. Further, a core exists if the measures are mutually absolutely continuous.
scientific article; zbMATH DE number 5373429