Complementary choice functions

TL;DR

This paper explores the theory of complementary choice functions, presenting three universal methods for their construction, which are relevant for matching problems with complementary contracts.

Contribution

It introduces three new universal methods for constructing complementary choice functions, expanding the theoretical framework for their application.

Findings

Three universal construction methods are proposed.

The methods include pre-topologies, direct images, and supermodular set-functions.

The work enhances understanding of choice functions in matching theory.

Abstract

The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three (universal) ways of constructing such functions are given: through pre-topologies, as direct images of completely complementary (or pre-ordered) choice functions, and with the help of supermodular set-functions.