PP-2019-30: Endriss, Ulle (2019) Analysis of One-to-One Matching Mechanisms via SAT Solving: Impossibilities for Universal Axioms. [Pre-print] (In Press)
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Abstract
We develop a powerful approach that makes modern SAT solving techniques available as a tool to support the axiomatic analysis of economic matching mechanisms. Our central result is a preservation theorem, establishing sufficient conditions under which the possibility of designing a matching mechanism meeting certain axiomatic requirements for a given number of agents carries over to all scenarios with strictly fewer agents. This allows us to obtain general results about matching by verifying claims for specific instances using a SAT solver. We use our approach to automatically de-rive elementary proofs for two new impossibility theorems: (i) a strong form of Roth’s classical result regarding the impossibility of designing mechanisms that are both stable and strategyproof and (ii) a result establishing the impossibility of guaranteeing stability while also respecting a basic notion of cross-group fairness (so-called gender-indifference).
| Item Type: | Pre-print |
|---|---|
| Report Nr: | PP-2019-30 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2019 |
| Additional Information: | game theory social choice theory automated reasoning |
| Subjects: | Computation Logic |
| Depositing User: | Ulle Endriss |
| Date Deposited: | 22 Dec 2019 12:14 |
| Last Modified: | 22 Dec 2019 12:14 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1725 |
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