No-Regret Learning in Dynamic Competition with Reference Effects Under Logit Demand
Authors: Mengzi Amy Guo, Donghao Ying, Javad Lavaei, Zuo-Jun Shen
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This work is dedicated to the algorithm design in a competitive framework, with the primary goal of learning a stable equilibrium. ... Despite the absence of typical properties required for the convergence of online games, such as strong monotonicity and variational stability, we demonstrate that under diminishing step-sizes, the price and reference price paths generated by OPGA converge to the unique SNE, thereby achieving the no-regret learning and a stable market. Moreover, with appropriate step-sizes, we prove that this convergence exhibits a rate of O(1/t). |
| Researcher Affiliation | Academia | Mengzi Amy Guo IEOR Department UC Berkeley mengzi_guo@berkeley.edu Donghao Ying IEOR Department UC Berkeley donghaoy@berkeley.edu Javad Lavaei IEOR Department UC Berkeley lavaei@berkeley.edu Zuo-Jun Max Shen IEOR Department UC Berkeley maxshen@berkeley.edu |
| Pseudocode | Yes | Algorithm 1 Online Projected Gradient Ascent (OPGA) |
| Open Source Code | No | The paper does not provide any statement or link indicating that source code for the described methodology is publicly available. |
| Open Datasets | No | The paper describes 'numerical experiments' but does not mention the use of any publicly available datasets. The experiments are based on simulated parameters, not real-world data with public access. |
| Dataset Splits | No | The paper describes numerical experiments, but these experiments do not involve real-world datasets with typical training, validation, and test splits. The paper focuses on theoretical convergence. |
| Hardware Specification | No | The paper describes numerical experiments but does not provide any specific details about the hardware (e.g., CPU, GPU models) used to run these experiments. |
| Software Dependencies | No | The paper describes theoretical algorithms and numerical experiments but does not specify any software dependencies with version numbers. |
| Experiment Setup | Yes | Figure 1: Price and reference price paths for Examples 1, 2, and 3, where the parameters are (a H, b H, c H) = (8.70, 2.00, 0.82), (a L, b L, c L) = (4.30, 1.20, 0.32), (r0 H, r0 L) = (0.10, 2.95), (p0 H, p0 L) = (4.85, 4.86), and α = 0.90. ... in Example 1 (see Figure 1a) corroborates Theorem 5.1 by demonstrating that the price and reference price trajectories converge to the unique SNE when we choose diminishing step-sizes that fulfill the criteria specified in Theorem 5.1. ... In particular, Example 1 (see Figure 1a) corroborates Theorem 5.1 by demonstrating that the price and reference price trajectories converge to the unique SNE when we choose diminishing step-sizes that fulfill the criteria specified in Theorem 5.1. By comparison, the over-large constant step-sizes employed in Example 2 (see Figure 1b) fails to ensure convergence, leading to cyclic patterns in the long run. |