On the Convergence of Tâtonnement for Linear Fisher Markets
Authors: Tianlong Nan, Yuan Gao, Christian Kroer
AAAI 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments are conducted to demonstrate that the theoretical linear convergence aligns with empirical observations. In this section, we demonstrate the convergence of tˆatonnement for the LFM and QLFM through numerical experiments. |
| Researcher Affiliation | Collaboration | 1Columbia University 2Microsoft EMAIL, EMAIL, EMAIL |
| Pseudocode | No | The paper describes mathematical update rules, such as Eq. (4) and Eq. (6), but does not present these or any other procedures within explicitly labeled 'Pseudocode' or 'Algorithm' blocks. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code for the methodology described, nor does it provide links to any code repositories. |
| Open Datasets | Yes | We next test tˆatonnement on a large-scale instance constructed from a movie rating dataset (Dooms, De Pessemier, and Martens 2013; Nan, Gao, and Kroer 2023). |
| Dataset Splits | No | The paper mentions using 'randomly generated instances' and a 'movie rating dataset' for numerical experiments but does not specify any training/test/validation splits, proportions, or methodologies for partitioning these datasets. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., CPU, GPU models, memory, or cloud instances) used for running the experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies or their version numbers (e.g., programming languages, libraries, frameworks, or solvers) used for implementing the methods or running the experiments. |
| Experiment Setup | Yes | For each market class, instance size, and step size, we run tˆatonnement for a large number of iterations until the error residuals do not decrease further. We use the squared error norm, pt p* 2, as the measure of convergence. ... As can be seen from Figs. 1 to 3, under both linear utilities and QL utilities, tˆatonnement with all stepsizes converges to a small neighborhood around the equilibrium prices for all instances. Moreover, larger stepsizes lead to faster initial convergence, but higher final error levels. |