arXiv subjects

Alessandro Rivello

Publications and source records attributed to Alessandro Rivello.

2 recordsLinked to original sources

arXiv2020

Connected Incomplete Preferences

This paper explores a new class of incomplete preferences -- termed ``connected preferences'' -- in which maximal domains of comparability are topologically connected. We provide necessary and sufficient conditions for continuous preferences to be connected. We also characterize their maximal domains of comparability. Our results extend classical findings in decision theory by linking topological properties of the choice space with the structure of preferences, offering a novel perspective on incompleteness in economic models.

econ.TH↗

arXiv2020

A Maximum Theorem for Incomplete Preferences

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.

econ.TH↗