Efficient and fair trading mechanisms on the full preference domain

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.