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

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  • Pinaki Mandal

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.

Suggested Citation

  • Pinaki Mandal, 2023. "Compatibility between Stability and Strategy-Proofness: A Single-Peaked Preferences Investigation," Papers 2304.11494, arXiv.org, revised Jul 2025.
    • Handle: RePEc:arx:papers:2304.11494
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