Existence of Myopic-Farsighted Stable Sets in Matching Markets
Bibliographic record
Abstract
In the context of one-to-one matching markets, we study myopic-farsighted stable sets, which are internally and externally stable when myopic agents consider immediate payoffs from their deviations, while farsighted agents anticipate counter-deviations and consider final payoffs. We constructively prove the existence of a (rational expectations) myopic-farsighted stable set, in which farsighted agents receive a single payoff while myopic agents may receive multiple payoffs. Our existence result extends to settings with enforcing coalitions of arbitrary size, yielding coalitional myopic-farsighted stable sets, and to settings where not all members of an enforcing coalition must strictly gain, yielding myopic-farsighted weakly stable sets. When all farsighted agents have unit demand, our results also extend to many-to-one matching markets. As a key corollary, we provide a foundation for the efficiency-adjusted deferred acceptance algorithm by showing that its outcome constitutes a singleton myopic-farsighted stable set when one side is farsighted and the other is myopic.
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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 | 0.005 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.006 | 0.006 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 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".