No-regret Learning in Price Competitions under Consumer Reference Effects
Authors: Negin Golrezaei, Patrick Jaillet, Jason Cheuk Nam Liang
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We study long-run market stability for repeated price competitions between two firms, where consumer demand depends on firms posted prices and consumers price expectations called reference prices. Consumers reference prices vary over time according to a memory-based dynamic, which is a weighted average of all historical prices. We show that if the firms run no-regret algorithms, in particular, online mirror descent (OMD), with decreasing step sizes, the market stabilizes in the sense that firms prices and reference prices converge to a stable Nash Equilibrium (SNE). Interestingly, we also show that there exist constant step sizes under which the market stabilizes. We further characterize the rate of convergence to the SNE for both decreasing and constant OMD step sizes. |
| Researcher Affiliation | Academia | Negin Golrezaei MIT Sloan School of Management golrezae@mit.edu Patrick Jaillet MIT Electrical Engineering and Computer Science jaillet@mit.edu Jason Cheuk Nam Liang MIT Operations Research Center jcnliang@mit.edu |
| Pseudocode | Yes | Algorithm 1 2-firm OMD pricing under reference price updates; Algorithm 2 Induced 3-firm OMD pricing with no reference price |
| Open Source Code | No | The paper does not include any statement about releasing source code for the methodology, nor does it provide a link to a code repository. |
| Open Datasets | No | The paper uses a theoretical model and parameters for numerical illustrations (e.g., "Consider the following demand and reference update model parameters: α = (5, 6), β = (2, 3), δ = (0.4, 0.7), γ = (0.1, 0.5), θ1 = 0.8, a = 0.4, P = [1, 2], and initial prices (p1, r1) = (1, 1, 1.5)."). It does not use or provide access to any publicly available empirical dataset. |
| Dataset Splits | No | The paper focuses on theoretical analysis and numerical illustrations with synthetic parameters. It does not conduct experiments on real datasets that would require train/validation/test splits. |
| Hardware Specification | No | The paper describes theoretical models and numerical examples. It does not mention any specific hardware used for simulations or computations. |
| Software Dependencies | No | The paper focuses on theoretical models and algorithms. It does not list any specific software dependencies or version numbers required for implementation or simulation. |
| Experiment Setup | Yes | Example 1 and 2 describe the parameters used for the demand and reference update model (e.g., "α = (5, 6), β = (2, 3), δ = (0.4, 0.7), γ = (0.1, 0.5), θ1 = 0.8, a = 0.4, P = [1, 2], and initial prices (p1, r1) = (1, 1, 1.5).") and the step size sequences for the OMD algorithm (e.g., "ϵi,t = 0.1/t^2", "ϵi,t = 1/t", "ϵi,t = (1-a)/βi"). |