We present a polynomial-time algorithm for computing a $1/e$-approximate Hylland--Zeckhauser (HZ) equilibrium. This establishes the \emph{first} efficient approximation guarantee for HZ equilibria in settings with multi-valued utilities. Our main technical contribution is a novel utility stratification technique that reduces the original multi-valued market to a structured bi-valued instance. This reduction allows us to efficiently compute the approximation by leveraging the exact algorithm of Vazirani and Yannakakis.

翻译：我们提出了一种多项式时间算法，用于计算$1/e$近似的海兰德-泽克豪泽均衡。这建立了在多值效用设定下海兰德-泽克豪泽均衡的**首个**高效逼近保证。我们的主要技术贡献是一种新颖的效用分层技术，该技术将原始多值市场简化为一个结构化的双值实例。通过利用Vazirani和Yannakakis的精确算法，这一化简使得我们能够高效地计算该近似值。