Constant Approximation for Hylland--Zeckhauser Equilibria

2026-06-04

AI Summary

This work addresses the long-standing lack of efficient approximation algorithms for computing Hylland–Zeckhauser (HZ) equilibria in markets with multi-valued utilities. The authors introduce a novel technique termed “utility stratification,” which transforms a multi-valued market into a structured binary instance. By integrating this reduction with the exact algorithm of Vazirani and Yannakakis, they achieve the first polynomial-time algorithm that computes a $1/e$-approximate HZ equilibrium. This result not only provides the first constant-factor approximation guarantee for HZ equilibria under multi-valued utilities but also establishes a new paradigm for solving complex market equilibrium problems through problem reduction.

Abstract

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.

Problem

• Hylland–Zeckhauser equilibrium
• approximation
• multi-valued utilities
• market equilibrium
• computational complexity

Innovation

• Hylland–Zeckhauser equilibrium
• approximation algorithm
• utility stratification
• multi-valued utilities
• market equilibrium