Strategy-Proofness in the Stable Matching Problem with Couples
Bibliographic record
Abstract
Stable matching problems (SMPs) arising in real-world markets often have extra complementarities in the participants' preferences. These complementarities break many of the theoretical properties of SMP and make it computationally hard to find a stable matching. A common complementarity is the introduction of couples in labor markets, which gives rise to the stable matching problem with couples (SMP-C). A major concern in markets is strategy-proofness since markets that are easily manipulated often unravel. In this paper we provide some key insights into the issue of strategy-proofness in SMP-C. We provide theoretical results that relate the set of resident Pareto optimal stable matchings (ℜ℘opt) admitted by an SMP-C instance to the ability of the residents to manipulate. We show that a mechanism returning an ℜ℘opt matching is, in certain cases, strategy-proof against residents attempting to manipulate by truncating their preference lists. We provide an algorithm for finding an ℜ℘opt matching when one exists. And finally, we study empirically the frequency of multiple stable and multiple ℜ℘opt matchings as the market sizes grows, and under different proportions of couples in the market. Our empirical results indicate that SMPC becomes less susceptible to manipulation as both the size of the market grows and the fraction of couples in the market shrinks.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.045 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".