Auctions on networks: Efficiency, consensus, passivity, rates of convergence
Bibliographic record
Abstract
First, a quantized progressive second price (PSP) auction mechanism called the Unique Limit Quantized - PSP (UQ-PSP) is presented for the allocation of fixed or timevarying quantities of a resource among arbitrary populations of agents. It is shown that (i) the states (i.e. bid prices and quantities) of the corresponding iterative dynamical auction system converge to a unique quantized (Nash) equilibrium with a common limit price for all agents, (ii) the limit price of all system trajectories is independent of the initial data, and (iii) modulo the quantization level, the limiting resource allocation is efficient, that is to say the corresponding social welfare function is optimized. Second, distributed auctions on a twolevel network are developed: each vertex in the higher level network is regarded as a supplier for a uniquely associated lower level network; each such lower level network consists of a set of agents which represent buyers; and each of the lower level networks and their associated suppliers is assumed to constitute a local UQ-PSP auction A¿. The adjustment of the quantities supplied to any A¿is via a consensus-based dynamical system which exchanges quantities depending upon the limit prices of the local auctions in the (nearest neighbour) neighborhood of A¿in the higher level network. Convergence is established using a passivity property of UQ-PSP auctions and the system properties on those networks which are scale free random graphs are investigated.
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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 | 0.006 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".