利用乘法模型與正交擾動價格設置之需求學習演算法計算均衡定價

A demand learning algorithm using multiplicative model with equilibrium and orthogonally-perturbed price setup

黃文盈(Wen-Ying Huang)

指導教授 ： 李雨青

國立清華大學/工學院/工業工程與工程管理學系/碩士(2020年)

摘要

動態定價能藉由調整定價決策提高公司收益。我們考慮在穩定需求環境中，存在多間公司販賣單一種商品的均衡定價系統，並且將每一期的問題視為非合作賽局的納許均衡問題。在需求曲線的參數是未知的條件下，每間公司必須透過歷史資料估計環境需求曲線之參數。我們提出一個利用乘法模型與正交擾動價格設置的需求學習演算法，其能夠求出每間公司之價格策略並同時學習需求曲線之參數以及最大化收益。在演算法中，每間公司的目標即透過依序調整價格決策來達成最佳收益。本研究進行一系列的數值實驗來分析在不同設定下之演算法表現，並利用後悔函數來衡量表現。我們發現到雖然演算法利用線性最小平方法估計非線性之需求曲線參數，但演算法的表現仍然為佳，並且隨著時間到達一萬期週期後，收斂比率均高於百分之九十以上。最後，本演算法可應用於競爭市場中販賣單一種產品之動態定價問題。

關鍵字

動態定價 ； 需求學習 ； 資料驅動 ； 納許均衡

並列摘要

Dynamic pricing enables firms get more revenue by adjusting the price decision. We consider a periodic review equilibrium pricing system in which multiple firms competing in the market of single product in a stationary demand environment and regard the single-period problem as the Nash equilibrium problem under a non-cooperative game. The parameters of the demand model are not known a priori and each firm needs to estimate parameters of underlying demand model by observed data. We propose a demand learning algorithm assuming a multiplicative demand model with an equilibrium and orthogonally-perturbed price setup, which can learn and earn concurrently to solve for the pricing policy of each firm in the competition. In the algorithm, each firms' objective is to sequentially adjust prices to maximize revenues under demand uncertainty. This research conducts a series of numerical experiments to analyze the algorithm in different settings and measure the performance by regret. We observe that the performance of the algorithm is good even though the algorithm estimates the parameters of nonlinear demand curves, logit and exponential models, by the linear least square method and show that the fraction of optimal revenues are above 90% as time goes by 10000 periods. Our algorithm can be applied to dynamic pricing problem with unknown demand for selling single product in a competitive market.

並列關鍵字

dynamic pricing ； demand learning ； data driven ； Nash equilibrium

參考文獻

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