Analysis of a class of decentralized dynamical systems: rapid convergence and efficiency of dynamical quantized auctions
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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).
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it