Compatibility between Stability and Strategy-Proofness: A Single-Peaked Preferences Investigation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916820055752704 |
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| author | Mandal, Pinaki |
| author_facet | Mandal, Pinaki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11494 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compatibility between Stability and Strategy-Proofness: A Single-Peaked Preferences Investigation Mandal, Pinaki Theoretical Economics 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. |
| title | Compatibility between Stability and Strategy-Proofness: A Single-Peaked Preferences Investigation |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2304.11494 |