Continuous linear utility for preferences on convex sets in normed real vector spaces. (English) Zbl 0980.91012
Summary: Let \(X\) be a nonempty convex set in a normed real vector space \((E,p)\) and let \(\precsim\) be a complete and transitive relation on \(X\). We specify conditions that are necessary and sufficient for \(\precsim\) to be representable by the restriction to \(X\) of a continuous linear functional \(V\) on \((E,p)\). The main result is applied to expected utility theory.
MSC:
| 91B08 | Individual preferences |
| 91B16 | Utility theory |
| 46N10 | Applications of functional analysis in optimization, convex analysis, mathematical programming, economics |
Keywords:
preferences; continuity; independence; continuous linear utility; exepcted utility; unboundednessReferences:
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