Abstraction pathologies in extensive games
Bibliographic record
Abstract
Extensive games can be used to model many scenarios in which multiple agents interact with an environment. There has been considerable recent research on finding strong strategies in very large, zero-sum extensive games. The standard approach in such work is to employ abstraction techniques to derive a more tractably sized game. An extensive game solver is then employed to compute an equilibrium in that abstract game, and the resulting strategy is presumed to be strong in the full game. Progress in this line of research has focused on solving larger abstract games, which more closely resemble the full game. However, there is an underlying assumption that by abstracting less, and solving a larger game, an agent will have a stronger strategy in the full game. In this work we show that this assumption is not true in general. Refining an abstraction can actually lead to a weaker strategy. We show examples of these abstraction pathologies in a small game of poker that can be analyzed exactly. These examples show that pathologies arise when abstracting both chance nodes as well as a player's actions. In summary, this paper shows that the standard approach to finding strong strategies for large extensive games rests on shaky ground.
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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 | 0.013 |
| 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 | 0.006 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 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".