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Closure and preferences. (English) Zbl 1434.91028

Summary: We investigate the results of D. M. Kreps [Econometrica 47, 565–577 (1979; Zbl 0423.90005)], dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satisfies Kreps’ axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by M. Richter and A. Rubinstein [“Back to fundamentals: equilibrium in abstract economies”, Am. Econ. Rev. 105, No. 8, 2570–2594 (2015; doi:10.1257/aer.20140270)].

MSC:

91B06 Decision theory
91B08 Individual preferences

Keywords:

menu; closure

Citations:

Zbl 0423.90005
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Full Text: DOI

References:

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