On the Relative Performance of Linear vs. Piecewise-Linear-Threshold Intertemporal Incentives
Bibliographic record
Abstract
This paper employs numerical simulations to compare the relative performance of linear contracts with piecewise-linear-threshold contracts in the case where the agent chooses actions over time. These contracts are restricted to be functions of the ending value of aggregate output. We find strong evidence that only linear contracts need be considered in comparison with piecewise-linear-threshold contracts in the situation where cumulative output is only updated periodically and the agent's utility function is exponential. This finding holds even when there are only two periods and hence one change of action by the agent. However, we find that the best piecewise-linear-threshold contract is significantly superior to the best linear contract when the agent has a power utility function. These numerical simulations also call into question the use of a cap when the agent's compensation is based on the ending value of aggregate output and the agent's effort takes place over time.
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How this classification was reachedexpand
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 | 0.004 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".