Bilateral Trade: A Regret Minimization Perspective
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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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 | 0.018 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.009 | 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 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".