Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium
Authors: Luofeng Liao, Christian Kroer
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments with synthetic and semi-real data verify our theory. Numerical experiments demonstrate the validity of the theory. We provide simulations and a semi-synthetic experiment based on a real-time bidding dataset from i Pin You (Liao et al., 2014). |
| Researcher Affiliation | Academia | 1IEOR, Columbia University. Correspondence to: Luofeng Liao <ll3530@columbia.edu>. |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain an explicit statement offering open-source code for the methodology described, nor does it provide a link to a code repository. |
| Open Datasets | Yes | Semi-real experiments. In App B.2 we construct realistic instances from real-world auction markets based on the i Pin You dataset (Liao et al., 2014). The i Pin You dataset (Liao et al., 2014) contains raw log data of the bid, impression, click, and conversion history on the i Pin You platform... |
| Dataset Splits | No | The paper mentions generating advertisers for simulation and analyzing finite-sample distributions but does not specify training, validation, and test splits for evaluating the core equilibrium models or bootstrap procedures in a standard machine learning context. The focus is on statistical properties rather than typical dataset splits. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., GPU/CPU models, memory) used to run the experiments. |
| Software Dependencies | No | The paper mentions the use of "MOSEK" for computing finite FPPEs, and "dual averaging" method, but it does not specify version numbers for MOSEK or any other software, libraries, or programming languages used. |
| Experiment Setup | Yes | The estimator requires an initial consistent estimate of the Hessian matrix, which is implemented with finite difference in Eq (16) with differencing stepsize ϵ = t 0.4. The estimator also requires a bootstrap stepsize ϵt = t d. We try d over the grid {0.4, 0.3, 0.2, 0.1, 0.05}. An experiment has parameters (t, n, d, α). Here t {100, 300, 500} is the number of items and n {10, 20, 30, 50} the number of advertisers. Parameter d is the exponent of the bootstrap stepsize, and α {0.1, 0.3, 0.5} is the proportion of advertisers that are not budget-constrained (i.e., β = 1). |