Specifying a game-theoretic extensive form as an abstract 5-ary relation
Bibliographic record
Abstract
Abstract This paper specifies an extensive form as a 5-ary relation (that is, as a set of quintuples) which satisfies eight abstract axioms. Each quintuple is understood to list a player, a situation (that is, a name for an information set), a decision node, an action, and a successor node. Accordingly, the axioms are understood to specify abstract relationships between players, situations, nodes, and actions. Such an extensive form is called a “pentaform”. Finally, a “pentaform game” is defined to be a pentaform together with utility functions. To ground this new specification in the literature, the paper defines the concept of a “traditional game” to represent the literature’s many specifications of finite-horizon and infinite-horizon games. The paper’s main result is to construct an intuitive bijection between pentaform games and traditional games. Secondary results concern disaggregating pentaforms by subsets, constructing pentaforms by unions, and initial pentaform applications to Selten subgames and perfect-recall (an extensive application to dynamic programming is in Streufert (Dynamic programming for pure-strategy subgame perfection in an arbitrary game. arXiv:2302.03855v3 , 2023)).
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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 | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".