Additive representation of separable preferences over infinite products View Full Text


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Article Info

DATE

2014-06

AUTHORS

Marcus Pivato

ABSTRACT

Let X be a set of outcomes, and let I be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order (≽) on XI admits an additive representation. That is: there exists a linearly ordered abelian group R and a ‘utility function’ u:X⟶R such that, for any x,y∈XI which differ in only finitely many coordinates, we have x≽y if and only if ∑i∈Iu(xi)-u(yi)≥0. Importantly, and unlike almost all previous work on additive representations, this result does not require any Archimedean or continuity condition. If (≽) also satisfies a weak continuity condition, then the paper shows that, for anyx,y∈XI, we have x≽y if and only if ∗∑i∈Iu(xi)≥∗∑i∈Iu(yi). Here, ∗∑i∈Iu(xi) represents a nonstandard sum, taking values in a linearly ordered abelian group ∗R, which is an ultrapower extension of R. The paper also discusses several applications of these results, including infinite-horizon intertemporal choice, choice under uncertainty, variable-population social choice and games with infinite strategy spaces. More... »

PAGES

31-83

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  • Journal

    TITLE

    Theory and Decision

    ISSUE

    1

    VOLUME

    77

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11238-013-9391-2

    DOI

    http://dx.doi.org/10.1007/s11238-013-9391-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1014244401


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