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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.12804 |
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Table of 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.