Multi-item auctions and fair division
Why this work is in the frame
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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
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.004 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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