這項研究的主要意義在於透過Python 程式語言撰寫程式進行線上比
例反應演算法的實際驗證。我們在建置之環境中實現了將比例反應方法應
用在線上費雪市場，並在其之下進行了嚴格的測試。通過廣泛的實驗和分
析，我們展示了演算法的表現如何與理論預測一致。本文的重點是展示演
算法在真實環境中的行為，以及它應對線上費雪市場所面臨挑戰的能力。
通過將我們的演算法中獲得的效用和市場均衡解的效用進行比較，我們提
供了具體的證據來證明其效果和效率。Python 為我們提供了一個研究和了
解演算法在市場環境有不同噪聲分布下行為的環境。我們在不同設置中進
行實驗，每個設置代表費雪市場中不同的情境，確保全面評估演算法的表
現。總的來說，我們在Python 建置之測試環境與框架下獲得了寶貴的見
解，了解了演算法的優勢和限制。這種實證分析是驗證和改進演算法的關
鍵步驟，有助於其在真實世界應用中的潛力，並推動線上市場機制設計領
域的發展。

The main significance of this study lies in the practical validation of the Online Proportional Response algorithm through Python programming. We implemented the proportional response method in an online Fisher market environment using Python and subjected it to rigorous testing. Through extensive experiments and analysis, we demonstrated how the algorithm’s performance aligns with theoretical predictions.
The focus of this paper is to showcase the behavior of the algorithm in a real-world environment and its ability to address challenges in the online Fisher market. By comparing the utility obtained from our algorithm with the utility of market equilibrium solutions, we provide concrete evidence of its effectiveness and efficiency.
Python provided us with an environment for studying and understanding
how the algorithm behaves in market environments with different noise
distributions. We conducted experiments in various settings, each representing different scenarios in the online Fisher market, ensuring a comprehensive evaluation of the algorithm’s performance.
In summary, we gained valuable insights within the testing environment
and framework built using Python, understanding the strengths and limitations of the algorithm. This empirical analysis is a crucial step in validating and improving the algorithm, contributing to its potential in real-world applications and advancing the field of online market mechanism design.

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