Analysis of a class of decentralized dynamical systems: rapid convergence and efficiency of dynamical quantized auctions
Bibliographic record
Abstract
In this paper, we study a class of progressive second price (PSP) auctions introduced by Lazar & Semret (1999, Design and analysis of the progressive second price auction for network bandwidth sharing. Technical Report 487-98-21. Columbia University Center for Telecommunications Research.) subject to various quantized pricing assumptions. The general PSP mechanism is employed here for the allocation of a divisible resource among arbitrary populations of agents in terms of two specific algorithms which are called, respectively, the aggressive–defensive qunatized progressive second price (ADQ-PSP) algorithm and the unique limit quantized progressive second price (UQ-PSP) algorithm, each of which derives from an associated set of quantized strategies. First, for the ADQ-PSP auction algorithm applied to agent populations with randomly and possibly widely distributed demand functions, it is shown that the states (i.e. bid prices and quantities) of the corresponding dynamical systems rapidly converge with high probability to a quantized (Nash) equilibrium with a common price for all agents. Second, for the UQ-PSP auction algorithm (developed as a modification of the ADQ-PSP algorithm) applied to general agent populations, the corresponding dynamical systems are such that (i) the limit price of all system trajectories is independent of the initial data and (ii) modulo the quantization level, the limiting resource allocation is efficient (i.e. the corresponding social welfare function, or summed individual valuation functions, is optimal).
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".