利用數據驅動計算非合作賽局之定價均衡的數值實驗

Experiment of a data-driven equilibrium pricing algorithm in a non-cooperative game

李喬瑋(Chiao-Wei Li)

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

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。

關鍵字

需求學習 ； 動態訂價 ； 奈許均衡 ； 線上學習 ； 賽局理論

並列摘要

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.

並列關鍵字

demand learning ； dynamic pricing ； Nash equilibrium ； online learning ； game theory ； aggregation

參考文獻

Arrow, K. J., & Debreu, G. (1954). Existence of an equilibrium for a competitive economy. Econometrica: Journal of the Econometric Society, 265-290.

Bertsimas, D., & Perakis, G. (2006). Dynamic pricing: A learning approach. In Mathematical and computational models for congestion charging (pp. 45-79). Springer, Boston, MA.

Besbes, O., & Zeevi, A. (2009). Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms. Operations Research, 57(6), 1407-1420.

Besbes, O., & Zeevi, A. (2015). On the (surprising) sufficiency of linear models for dynamic pricing with demand learning. Management Science, 61(4), 723-739.

Bitran, G. R., & Mondschein, S. V. (1997). Periodic pricing of seasonal products in retailing. Management science, 43(1), 64-79.