Bibliographic record
Abstract
In this article, we study the problem of online market clearing where there is one commodity in the market being bought and sold by multiple buyers and sellers whose bids arrive and expire at different times. The auctioneer is faced with an online clearing problem of deciding which buy and sell bids to match without knowing what bids will arrive in the future. For maximizing profit , we present a (randomized) online algorithm with a competitive ratio of ln( p max − p min ) + 1, when bids are in a range [ p min , p max ], which we show is the best possible. A simpler algorithm has a ratio twice this, and can be used even if expiration times are not known. For maximizing the number of trades, we present a simple greedy algorithm that achieves a factor of 2 competitive ratio if no money-losing trades are allowed. We also show that if the online algorithm is allowed to subsidize matches---match money-losing pairs if it has already collected enough money from previous pairs to pay for them---then it can actually be 1-competitive with respect to the optimal offline algorithm that is not allowed subsidy. That is, for maximizing the number of trades, the ability to subsidize is at least as valuable as knowing the future. We also consider objectives of maximizing buy or sell volume and social welfare. We present all of these results as corollaries of theorems on online matching in an incomplete interval graph.We also consider the issue of incentive compatibility, and develop a nearly optimal incentive-compatible algorithm for maximizing social welfare. For maximizing profit , we show that no incentive-compatible algorithm can achieve a sublinear competitive ratio, even if only one buy bid and one sell bid are alive at a time. However, we provide an algorithm that, under certain mild assumptions on the bids, performs nearly as well as the best fixed pair of buy and sell prices, a weaker but still natural performance measure. This latter result uses online learning methods, and we also show how such methods can be used to improve our “optimal” algorithms to a broader notion of optimality. Finally, we show how some of our results can be generalized to settings in which the buyers and sellers themselves have online bidding strategies, rather than just each having individual bids.
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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 | 0.003 | 0.016 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.028 | 0.006 |
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".