Abstract
For every integrable allocation (X 1,X 2, ...,X n ) of a random endowmentY=Σ =1/n i X i amongn agents, there is another allocation (X 1*,X 2*, ...,X n *) such that for every 1≤i≤n,X i * is a nondecreasing function ofY (or, (X 1*,X 2*, ...,X n *) areco-monotone) andX i * dominatesX i by Second Degree Dominance.
If (X 1*,X 2*, ...,X n *) is a co-monotone allocation ofY=Σ =1/n i X i *, then for every 1≤i≤n, Y is more dispersed thanX i * in the sense of the Bickel and Lehmann stochastic order.
To illustrate the potential use of this concept in economics, consider insurance markets. It follows that unless the uninsured position is Bickel and Lehmann more dispersed than the insured position, the existing contract can be improved so as to raise the expected utility of both parties, regardless of their (concave) utility functions.
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Landsberger, M., Meilijson, I. Co-monotone allocations, Bickel-Lehmann dispersion and the Arrow-Pratt measure of risk aversion. Ann Oper Res 52, 97–106 (1994). https://doi.org/10.1007/BF02033185
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DOI: https://doi.org/10.1007/BF02033185