Natural interviewing equilibria in matching settings
Bibliographic record
Abstract
Abstract A common assumption in matching markets is that both sides fully know their preferences. However, when there are many participants this may be neither realistic nor feasible. Instead, agents may have some partial (perhaps stochastic) information about alternatives and will invest time and resources to better understand the inherent benefits and tradeoffs of different choices. Using the framework of matching medical residents with hospital programs, we study strategic behaviour by residents in a setting where hospitals maintain a publicly known master list of residents (i.e., all hospitals have an identical ranking of all the residents, for example, based on grades) and residents have to decide with which hospitals to interview, before submitting their preferences to the matching mechanism. We first show the existence of pure strategy equilibrium under very general conditions. We then study the setting when residents’ preferences are drawn from a known Mallows distribution. We prove that assortative equilibrium ( k top residents interview with k top hospitals, etc.) arises only when residents interview with a small number of programs. Surprisingly, such equilibria (or even weaker notions of assortative interviewing) do not exist when residents can interview with many hospital programs, even when residents’ preferences are very similar. Simulations on possible outcome equilibrium indicate that some residents will pursue a reach/safety strategy.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".