The Hylland-Zeckhauser gave a classic pricing-based mechanism (HZ) for a one-sided matching market; it yields allocations satisfying Pareto optimality and envy-freeness (Hylland and Zeckhauser, 1979), and the mechanism is incentive compatible in the large (He et al., 2018). They also studied the exchange extension of HZ and gave an example showing that it may not even admit an equilibrium. In this paper, we consider two models of two sided matching markets: when utility functions are symmetric and when they are non-symmetric. We ask if these models always admit allocations satisfying the two basic properties of Pareto efficiency and envy freeness. Our results are negative. A corollary of the former result is a negative result for non-bipartite matching markets as well.

翻译：Hylland-Zeckhauser针对单边匹配市场提出了经典的基于定价机制（HZ），该机制能够产生满足帕累托最优性和无嫉妒性的分配（Hylland and Zeckhauser, 1979），且该机制在大规模市场中具有激励相容性（He et al., 2018）。他们还研究了HZ机制的交换扩展，并通过实例表明该扩展甚至可能不存在均衡。本文考虑了双边匹配市场的两种模型：效用函数对称与非对称情形。我们探究这些模型是否始终存在同时满足帕累托有效性和无嫉妒性这两个基本属性的分配。研究结果是否定的。前一个结果的推论同样适用于非二分匹配市场。