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A Maximum Theorem for Incomplete Preferences

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  • Leandro Gorno
  • Alessandro Rivello

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.

Suggested Citation

  • Leandro Gorno & Alessandro Rivello, 2020. "A Maximum Theorem for Incomplete Preferences," Papers 2007.09781, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:2007.09781
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    References listed on IDEAS

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