Reconsidering the Existence of Stable Solutions in Three-sided Matching Problems with Mixed Preferences

We reexamine the existence of stable solutions in a class of three-sided matching problems previously studied by Zhang and Zhong (2021). The sets of participants are U, V, and W. Agents in U have strict preferences defined on V, agents in V have strict preferences defined on W, and agents in W have strict preferences defined on UxV. In this framework, we show that a weakly stable matching may not exist. Despite this, we algorithmically show that a stable matching exists when agents in W are interested in the first place in agents in V