A complete characterization of equilibria in an intrinsic common agency screening game
Bibliographic record
Abstract
We characterize the complete set of equilibrium allocations to an intrinsic common agency screening game as the set of solutions to self-generating optimization programs. We provide a complete characterization of equilibrium outcomes for regular environments by relying on techniques developed elsewhere for aggregate games and for the mechanism design delegation literature. The set of equilibria include those with non-differentiable payoffs and discontinuous choices, as well as equilibria that are smooth and continuous in types. We identify one equilibrium, the maximal equilibrium, which is the unique solution to a self-generating optimization program with the largest (or "maximal") domain, and the only equilibrium that is supported with bi-conjugate (i.e., least-concave) tariffs. The maximal equilibrium exhibits a n-fold distortion caused by each of the n principal's non-cooperative behavior in over-harvesting the agent's information rent. Furthermore, in any equilibrium, over any interval of types in which there is full separation, the agent's equilibrium action corresponds to the allocation in the maximal equilibrium. Under reasonable conditions, the maximal equilibrium maximizes the agent's information rent within the class of equilibrium allocations. When the principals' most-preferred equilibrium allocation differs from the maximal equilibrium, we demonstrate that the agent's choice function exhibits an interval of bunching over the worst agent types, and elsewhere corresponds with the maximal allocation. The optimal region of bunching trades off the principals' desire to constrain inefficient n-fold marginalizations of the agent's rent against the inefficiency of pooling agent types.
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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".