Multi-item auctions and fair division
Bibliographic record
Abstract
The question of how to divide a collection of items amongst a set of agents is of central importance to society.There are two main directions from which this question is approached: a game-theoretic direction that studies the mechanisms -primarily auctionsthat are used to divide items amongst agents, and a normative direction that studies the existence and computability of allocations that have desirable properties like fairness and high social welfare.In this thesis, we detail our contributions to both areas.In Part I of this thesis, we analyze two prominent multi-item auctions, the sequential and simultaneous item-bidding auctions.We prove that the declining price anomaly is not guaranteed to hold in the equilibria of full-information sequential auctions with three or more buyers.We then analyze the risk-free profitability, i.e. the threshold payoff that a buyer can guarantee for itself, in sequential and simultaneous auctions, when the buyer's valuation function is in the subadditive set function class (and its subclasses).In Part II, we discuss our contributions to the fair division problem, focusing on the envy-free allocation of indivisible items along with payments.We prove two conjectures of Halpern and Shah [SAGT 2019] and present additional upper bounds on the total quantity of subsidy sufficient to guarantee envy-freeness in any instance.We then study the tradeoffs between transfer payments, fairness, and welfare.i √ 2 , f 2 (x), f (x) + 1 √ 3 and f 3 (x) . . . . . . .3.2 Plot of the Functions f (x), t 1 (x), t 2 (x), and t 3 (x): t * (x) is the piecewise linear function shown by the bold line segments . . . . . . . . . . . . . . . . . . . . . .
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".