Before revision:  * A rational convex program for HZ under dichotomous utilities; a combinatorial polynomial time algorithm for this case was given by Vazirani and Yannakakis (2020) . The \epsilon-approximate ADHZ model fills a void, described in the paper, in the space of general mechanisms for one-sided matching markets .
After revision:  Since computing an equilibrium for HZ is likely to be highly intractable and because of the difficulty of extending HZ to more general utility functions, Hosseini and Vazirani proposed (a rich collection of) Nash-bargaining-based matching market models. For the dichotomous-utilities case of their model linear Arrow-Debreu Nash bargaining one-sided matching markets .