[Paper Review] Hybrid Mechanisms: Trading off Efficiency and Strategyproofness in One-Sided Matching

Timo Mennle, Sven Seuken|arXiv (Cornell University)|Jan 1, 2014

Game Theory and Voting Systems31 references3 citations

TL;DR

This paper introduces hybrid mechanisms—convex combinations of existing one-sided matching mechanisms like Random Serial Dictatorship (RSD) and Probabilistic Serial (PS)—to trade off strategyproofness and efficiency. By combining mechanisms, the authors achieve improved ex-post efficiency over RSD while maintaining partial strategyproofness within a defined bound, with significant efficiency gains demonstrated numerically.

ABSTRACT

We study one-sided matching mechanisms where agents have vNM utility functions and report ordinal preferences. Strong impossibility results restrict the design space os strategyproof mechanisms in this domain. Improving on efficiency beyond the ex-post efficiency of Random Serial Dictatorship (RSD) generally requires trade-offs. In this paper, we introduce hybrid mechanisms, which are convex combinations of existing mechanism, and we show that they are a powerful yet simple method for trading off strategyproofness and efficiency. We present conditions under which hybrid mechanisms remain partially strategyproof with respect to a given bound for the degree of strategyproofness. At the same time, these hybrids have better efficiency properties than the less efficient component. Our approach can be successfully applied to create hybrids of RSD and the Probabilistic Serial mechanism (PS), as well as hybrids of RSD and the adaptive Boston mechanism (ABM). We provide numerical results demonstrating that the improvements can be significant. 1.

Motivation & Objective

• To address the inherent trade-off between strategyproofness and efficiency in one-sided matching mechanisms with ordinal preferences.
• To overcome strong impossibility results limiting strategyproof mechanisms in the vNM utility domain.
• To design a flexible framework for combining existing mechanisms that improves efficiency without fully sacrificing strategyproofness.
• To demonstrate that convex combinations of mechanisms (hybrids) can yield better efficiency than individual components while retaining partial strategyproofness.

Proposed method

• The authors define hybrid mechanisms as convex combinations of two or more base mechanisms, such as RSD and PS or RSD and ABM.
• They establish conditions under which these hybrids remain partially strategyproof, bounded by a specified degree of strategyproofness.
• The approach leverages the ex-post efficiency of RSD and the higher efficiency of PS or ABM to create mechanisms with improved social welfare.
• Theoretical analysis derives bounds on strategyproofness based on the mixing parameter, ensuring that manipulation incentives remain limited.
• Numerical experiments evaluate the efficiency and strategyproofness trade-offs across different hybrid configurations.
• The framework is applied to concrete mechanisms: RSD-PS and RSD-ABM hybrids, with performance measured via expected social welfare and strategyproofness metrics.

Experimental results

Research questions

• RQ1 Can convex combinations of existing mechanisms improve efficiency beyond the ex-post efficiency of RSD while preserving partial strategyproofness?
• RQ2 What conditions ensure that hybrid mechanisms remain strategyproof up to a given bound?
• RQ3 How do RSD-PS and RSD-ABM hybrids compare in terms of efficiency and strategyproofness?
• RQ4 What is the maximum efficiency gain achievable through hybrid mechanisms without fully compromising strategyproofness?
• RQ5 Can numerical results confirm significant efficiency improvements in practical settings?

Key findings

• Hybrid mechanisms combining RSD and PS achieve higher ex-post efficiency than RSD alone, with measurable improvements in expected social welfare.
• The hybrids maintain partial strategyproofness, with manipulation incentives bounded by a defined threshold, depending on the mixing parameter.
• Significant efficiency gains are observed in numerical evaluations, particularly in settings with high preference overlap.
• The hybrid framework allows for systematic trade-offs between strategyproofness and efficiency, enabling mechanism designers to calibrate the balance.
• The approach is generalizable and successfully applied to both PS and ABM, demonstrating robustness across different base mechanisms.