近年來動態定價演算法已廣泛使用於價格決策上。我們考慮在未知環境需求曲線的條件下，存在販賣同一商品且相互競爭的多間公司，並假設此需求曲線僅與自身與競爭者之訂價策略有關。本研究設計出一套資料驅動均衡價格演算法並利用歷史資料進行環境需求曲線的估計及最佳化公司利益。在本實驗中我們比較在不同環境假設的狀況下此演算法的收斂情形及探討競爭環境中存在已知公司與否對演算法之影響，並進一步針對歷史資料使用量的差異與估計的準確度進行分析。從數值實驗的結果中可發現各環境假設條件下，在經過一定時間後此演算法之收斂比率均可達百分之九十五以上，因此可由此說明在相互競爭且未知環境需求曲線的賽局中，無論各公司真實環境需求曲線形式為何，均可透過此演算法進行估計及價格決策。

In recent research, demand learning and dynamic pricing algorithm have widely applied in making pricing strategies. We consider a periodic-review pricing problem where there are N firms competing in the market of a commodity in a stationary demand environment. The firm’s demand consists of a linear model which is conditional on both its selling prices and other firms’ with an independent and identically random noise. We design a data-driven equilibrium pricing algorithm where each firm can modify the price over discretized time without knowing the underlying demand function. Each firm’s objective is to sequentially set prices to maximize revenues under demand uncertainty and competition. We conduct the numerical experiments to realize the effectiveness of the algorithm in well specified and misspecified settings. We observe that the fraction of optimal price can reach at least 95% after 10000 periods regardless of the setting of environment and the number of competitors in the market. In other words, our research reveal that no matter what form the true underlying demand curve is, the firms are able to make their pricing strategies well by the algorithm.

Contents
Abstract------------------------------------------------------- i
摘要------------------------------------------------------------ii
List of Tables------------------------------------------------- v
List of Figures------------------------------------------------ vi
Chapter 1 Introduction---------------------------------------- 1
Chapter 2 Literature Review----------------------------------- 3
2.1 Dynamic Pricing Problem------------------------------------ 3
2.2 Demand Learning-------------------------------------------- 4
2.3 Generalized Nash Equilibrium Problems---------------------- 5
2.4 Learning and Pricing in a Competitive Environment---------- 7
Chapter 3 Model----------------------------------------------- 9
3.1 Environment------------------------------------------------ 9
3.2 Algorithm-------------------------------------------------- 11
Chapter 4 Numerical Experiment-------------------------------- 15
4.1 Performance Measure---------------------------------------- 15
4.2 Validating the Difference of Underlying Demand Function---- 16
4.3 Validating the Impact of the Firm with Known Demand Function
--------------------------------------------------------------- 23
4.4 Validating the Effectiveness of Aggregation---------------- 28
Chapter 5 Conclusions and the Future Work---------------------- 32
References----------------------------------------------------- 34

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