The implications of finite‐order reasoning
Bibliographic record
Abstract
The epistemic conditions of rationality and mth‐order strong belief of rationality (R mSBR; Battigalli and Siniscalchi, 2002) formalize the idea that players engage in contextualized forward‐induction reasoning. This paper characterizes the behavior consistent with R mSBR 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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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 | 0.012 | 0.067 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.014 |
| Scholarly communication | 0.004 | 0.013 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.006 |
| 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".