Relational Contracts, Multiple Agents, and Correlated Outputs
Bibliographic record
Abstract
We analyze relational contracts between a principal and a set of risk-neutral agents whose outputs are correlated. When only the agents’ aggregate output can be observed, a team incentive scheme is shown to be optimal, where each agent is paid a bonus for aggregate output above a threshold. We show that the efficiency of the team incentive scheme depends on the way in which the team members’ outputs are correlated. The reason is that correlation affects the variance of total output and thus, the precision of the team’s performance measure. Negatively correlated contributions reduce the variance of total output, and this improves incentives for each team member in the setting that we consider. This also has implications for optimal team size. If the team members’ outputs are negatively correlated, more agents in the team can improve efficiency. We then consider the case where individual outputs are observable. A tournament scheme with a threshold is then optimal, where the threshold depends on an agent’s relative performance. We show that correlation affects both the efficiency and design of the optimal tournament scheme. This paper was accepted by Shivaram Rajgopal, accounting.
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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 | 0.009 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".