Incentive Designs for Stackelberg Games with a Large Number of Followers\n and their Mean-Field Limits
Bibliographic record
Abstract
We study incentive designs for a class of stochastic Stackelberg games with\none leader and a large number of (finite as well as infinite population of)\nfollowers. We investigate whether the leader can craft a strategy under a\ndynamic information structure that induces a desired behavior among the\nfollowers. For the finite population setting, under convexity of the leader's\ncost and other sufficient conditions, we show that there exist symmetric\n\\emph{incentive} strategies for the leader that attain approximately optimal\nperformance from the leader's viewpoint and lead to an approximate symmetric\n(pure) Nash best response among the followers. Leveraging functional analytic\ntools, we further show that there exists a symmetric incentive strategy, which\nis affine in the dynamic part of the leader's information, comprising partial\ninformation on the actions taken by the followers. Driving the follower\npopulation to infinity, we arrive at the interesting result that in this\ninfinite-population regime the leader cannot design a smooth ``finite-energy''\nincentive strategy, namely, a mean-field limit for such games is not\nwell-defined. As a way around this, we introduce a class of stochastic\nStackelberg games with a leader, a major follower, and a finite or infinite\npopulation of minor followers. For this class of problems, we establish the\nexistence of an incentive strategy and the corresponding mean-field Stackelberg\ngame. Examples of quadratic Gaussian games are provided to illustrate both\npositive and negative results. In addition, as a byproduct of our analysis, we\nestablish the existence of a randomized incentive strategy for the class\nmean-field Stackelberg games, which in turn provides an approximation for an\nincentive strategy of the corresponding finite population Stackelberg game.\n
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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 | 0.005 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| 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".