The Machiavellian frontier of stable mechanisms
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916320294993920 |
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| author | Chen, Qiufu Li, Yuanmei Yin, Xiaopeng Zhang, Luosai Zhou, Siyi |
| author_facet | Chen, Qiufu Li, Yuanmei Yin, Xiaopeng Zhang, Luosai Zhou, Siyi |
| contents | The impossibility theorem in Roth (1982) states that no stable mechanism satisfies strategy-proofness. This paper explores the Machiavellian frontier of stable mechanisms by weakening strategy-proofness. For a fixed mechanism $φ$ and a true preference profile $\succ$, a $(φ,\succ)$-boost mispresentation of agent i is a preference of i that is obtained by (i) raising the ranking of the truth-telling assignment $φ_i(\succ)$, and (ii) keeping rankings unchanged above the new position of this truth-telling assignment. We require a matching mechanism $φ$ neither punish nor reward any such misrepresentation, and define such axiom as $φ$-boost-invariance. This is strictly weaker than requiring strategy-proofness. We show that no stable mechanism $φ$ satisfies $φ$-boost-invariance. Our negative result strengthens the Roth Impossibility Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12804 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Machiavellian frontier of stable mechanisms Chen, Qiufu Li, Yuanmei Yin, Xiaopeng Zhang, Luosai Zhou, Siyi Theoretical Economics The impossibility theorem in Roth (1982) states that no stable mechanism satisfies strategy-proofness. This paper explores the Machiavellian frontier of stable mechanisms by weakening strategy-proofness. For a fixed mechanism $φ$ and a true preference profile $\succ$, a $(φ,\succ)$-boost mispresentation of agent i is a preference of i that is obtained by (i) raising the ranking of the truth-telling assignment $φ_i(\succ)$, and (ii) keeping rankings unchanged above the new position of this truth-telling assignment. We require a matching mechanism $φ$ neither punish nor reward any such misrepresentation, and define such axiom as $φ$-boost-invariance. This is strictly weaker than requiring strategy-proofness. We show that no stable mechanism $φ$ satisfies $φ$-boost-invariance. Our negative result strengthens the Roth Impossibility Theorem. |
| title | The Machiavellian frontier of stable mechanisms |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2405.12804 |