Compatibility between Stability and Strategy-Proofness: A Single-Peaked Preferences Investigation

TL;DR

This paper investigates conditions under which stability and strategy-proofness can coexist in two-sided matching markets with single-peaked preferences, identifying compatible subdomains and highlighting inherent limitations.

Contribution

It characterizes all single-peaked preference subdomains where stability and strategy-proofness are compatible and proves an impossibility result for strong group strategy-proofness.

Findings

Identifies all single-peaked subdomains with compatible stability and strategy-proofness.

Provides a matching rule that achieves stability and weak/strong group strategy-proofness on these subdomains.

Shows the incompatibility between stability and strong group strategy-proofness in certain cases.

Abstract

In two-sided matching markets, ensuring both stability and strategy-proofness poses a significant challenge; it is impossible when agents' preferences are unrestricted. But what if agents' preferences have specific restricted structures? Such scenarios frequently arise in real-world applications. This study explores the possibility of achieving both stability and strategy-proofness by focusing on scenarios where agents' preferences follow a structured pattern called single-peakedness. We focus on the simplest case - the well-known marriage problem, which is a one-to-one matching market. Despite its simplicity, this model is a useful starting point for exploration in many cases. Our main contribution is identifying all single-peaked subdomains on which stability and (weak/strong group) strategy-proofness are compatible, which we present through two key results. The first one characterizes all single-peaked subdomains with stable and (weakly group) strategy-proof matching rules, and identifies such a matching rule on these domains. The second one is an impossibility result that shows the incompatibility between stability and strong group strategy-proofness on single-peaked subdomains.