Caller Number Five and Related Timing Games
Why this work is in the frame
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Bibliographic record
Abstract
There are two varieties of timing games in economics: wars of attrition, in which having more predecessors helps, and pre-emption games, in which having more predecessors hurts. This paper introduces and explores a spanning class with rank-order payoffs that subsumes both varieties as special cases. We assume time is continuous, actions are unobserved, and information is complete, and explore how equilibria of the games, in which there is shifting between phases of slow and explosive (positive probability) stopping, capture many economic and social timing phenomena. Inspired by auction theory, we first show how each symmetric Nash equilibrium is equivalent to a different "potential function.'' By using this function, we straightforwardly obtain existence and characterization results. Descartes' Rule of Signs bounds the number of phase transitions. We describe how adjacent timing game phases interact: war of attrition phases are not played out as long as they would be in isolation, but instead are cut short by pre-emptive atoms. We bound the number of equilibria, and compute the payoff and duration of each equilibrium.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.007 | 0.004 |
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