Non-parametric identification and testing of quantal response equilibrium
Bibliographic record
Abstract
This paper studies the falsifiability and identification of Quantal Response Equilibrium (QRE) when each player's utility and error distribution are relaxed to be unknown non-parametric functions. Using the variation of players' choices across a series of games, we first show that both the utility function and the distribution of errors are non-parametrically over-identified. This over-identification result further suggests a straightforward testing procedure for QRE which achieves the desired type-1 error and maintains a small type-2 error. To apply this methodology, we conduct an experimental study of the matching pennies game. Our non-parametric estimates strongly reject the conventional Logit choice probability. Moreover, when the utility and the error distribution are sufficiently flexible and heterogeneous, the quantal response hypothesis cannot be rejected for 70% of participants. However, strong assumptions such as linear utility, logistically distributed errors, and homogeneity lead to substantially higher rejection rates.
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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 | 0.103 | 0.402 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.008 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 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".