The implications of finite‐order reasoning
Why this work is in the frame
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Bibliographic record
Abstract
The epistemic conditions of rationality and m th‐order strong belief of rationality (R m SBR; Battigalli and Siniscalchi, 2002) formalize the idea that players engage in contextualized forward‐induction reasoning. This paper characterizes the behavior consistent with R m SBR across all type structures. In particular, in a class of generic games, R( m − 1)SBR is characterized by a new solution concept we call an m ‐best response sequence ( m ‐BRS). Such sequences are an iterative version of extensive‐form best response sets (Battigalli and Friedenberg, 2012). The strategies that survive m rounds of extensive‐form rationalizability are consistent with an m ‐BRS, but there are m ‐BRS's that are disjoint from the former set. As such, there is behavior that is consistent with R( m − 1)SBR but inconsistent with m rounds of extensive‐form rationalizability. We use our characterization to draw implications for the interpretation of experimental data. Specifically, we show that the implications are nontrivial in the three‐repeated Prisoner's Dilemma and Centipede games.
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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 | 0.002 | 0.006 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it