Efficient and fair trading mechanisms on the full preference domain

TL;DR

This paper extends existing trading mechanisms to accommodate indifferences in preferences, maintaining efficiency and fairness, and generalizes the probabilistic serial mechanism for house allocation without complex tools.

Contribution

It introduces a method to adapt trading mechanisms to the full preference domain, broadening their applicability while preserving key properties.

Findings

Mechanisms now handle indifferences in preferences.

Generalization of the probabilistic serial mechanism.

Maintains efficiency and fairness in broader settings.

Abstract

Yu and Zhang (2025) introduce a new method for defining trading mechanisms in market design and apply it to develop new mechanisms that achieve efficiency and fairness in various models. However, their assumption of strict preferences limits its applicability. This paper extends their approach to the full preference domain, allowing for indifferences while preserving key efficiency and fairness properties. As a corollary, we generalize the probabilistic serial mechanism in the house allocation model to the full preference domain without relying on operations research tools.