Bilateral Trade: A Regret Minimization Perspective
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Bibliographic record
Abstract
Bilateral trade, a fundamental topic in economics, models the problem of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. In this paper, we cast the bilateral trade problem in a regret minimization framework over T rounds of seller/buyer interactions, with no prior knowledge on their private valuations. Our main contribution is a complete characterization of the regret regimes for fixed-price mechanisms with different feedback models and private valuations, using as a benchmark the best fixed price in hindsight. More precisely, we prove the following tight bounds on the regret: [Formula: see text] for full-feedback (i.e., direct revelation mechanisms). [Formula: see text] for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities. [Formula: see text] for realistic feedback and seller/buyer valuations with bounded densities. [Formula: see text] for realistic feedback and independent seller/buyer valuations. [Formula: see text] for the adversarial setting. Funding: This work was partially supported by the European Research Council Advanced [Grant 788893] AMDROMA “Algorithmic and Mechanism Design Research in Online Markets”, the Ministero dell’Istruzione, dell’Università e della Ricerca PRIN project ALGADIMAR “Algorithms, Games, and Digital Markets”, the AI Interdisciplinary Institute ANITI (funded by the French “Investing for the Future—PIA3” program under the [Grant agreement ANR-19-PI3A-0004], the project BOLD from the French national research agency (ANR), the EU Horizon 2020 ICT-48 research and innovation action ELISE (European Learning and Intelligent Systems Excellence, [Grant agreement 951847].
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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 | 0.007 | 0.019 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.007 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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