A Maximum Theorem for Incomplete Preferences

Leandro Gorno and Alessandro Rivello

Papers from arXiv.org

Abstract: We extend Berge's Maximum Theorem to allow for incomplete preferences. We first provide a simple version of the Maximum Theorem for convex feasible sets and a fixed preference. Then, we show that if, in addition to the traditional continuity assumptions, a new continuity property for the domains of comparability holds, the limits of maximal elements along a sequence of decision problems are maximal elements in the limit problem. While this new continuity property for the domains of comparability is not generally necessary for optimality to be preserved by limits, we provide conditions under which it is necessary and sufficient.

Date: 2020-07, Revised 2021-11
New Economics Papers: this item is included in nep-mic
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Journal Article: A maximum theorem for incomplete preferences (2023)
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