Remarks concerning concave utility functions on finite sets
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A direct construction of concave utility functions representing convex preferences on finite sets is presented. An alternative construction in which at first directions of supergradients (“prices”) are found, and then utility levels and lengths of those supergradients are computed, is exhibited as well. The concept of a least concave utility function is problematic in this context.
Keywords and PhrasesConcave utility Finite sets Supergradients Afriat-Varian algorithm Least concavity
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