當賣方面對市場中的策略型消費者時，他必須做出幾個重要的決定來支持他的事業，例如他想要提供的折扣頻率和折扣深度，以便最大化他的利潤。在我們的日常生活中，我們經常會在購買商品時看到不同類型的促銷活動，特別是如果我們的產品有時效性。而這些不僅僅只是市場銷售策略，背後更重要的是賣家透過該策略來改變消費者對原本產品的效用。

賣家和消費者最困難的選擇是：選擇哪一個促銷手法對他們是最有利的？折扣幅度較大但是較少見的折扣，或是折扣幅度較小但是經常性的折扣？通常，人們更喜歡折扣幅度較大但不太頻繁的折扣，因為產品永久性的。但是，如果產品有時效性，並且我們假設賣方會隨著時間的推移打折因為產品有時效性，那麼我們如何知道哪種方法對賣方和消費者都更有利可圖？

為了解決與賣方和消費者決策相關的這些現象，我們建立了消費者剩餘模型，以在產品有時效性的條件和消費者為策略性消費者的情況下，找到最優折扣深度和最優折扣頻率。我們使用該模型分析具時效性的產品和折扣深度和折扣頻率的不同情況。

When seller face strategic consumers in the market, he has to make several important decisions to support his business, some of the important decisions are the discount frequency and discount depth that he wants to provide in order to maximize his profit. In our daily life, we often see different kinds of promotions when we purchase goods especially if our product is going to be obsolescent. The most difficult choice for both seller and consumer is : which one to choose? Deep but less frequent discount or little but frequently discount?
More importantly, these strategies are not just strategies, sellers use these strategies to change the consumer’s utility to the product.
Usually, people prefer deep but less frequent discount because the product is durable. However, if the product is going to be obsolescent, and we assume seller will make a discount as time goes by, then how do we know which method is more profitable both for seller and consumer?
To address this phenomenon related to both seller’s and consumer’s decision, we develop a model of consumer’s surplus to find the optimal discount depth and optimal discount frequency under the situation which the product is obsolescent and the consumer is strategic. We use the model to analyze the different cases to the obsolescent product and discount depth and discount frequency.

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dynamic price management for perishable foods on retailer performance in the presence of need-driven purchasing consumers", Kookmin University, Seoul, South Korea; and 2 University of Liverpool, Liverpool, UK,pp1180-1183
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Xiaohuan Wang Zhi-Ping Fan Yiming Wang Manning Li , 2015,"A laboratory
exploration for multi-period perishable food pricing", British Food Journal, Vol.
117 s 9 pp.6-10
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[21] Luis Briceño-Arias, José R. Correa, Andrés Perlroth,2017, " Optimal Continuous Pricing with Strategic Consumers", management science,pp.3-5
[22] Guillermo Gallego, Ming Hu (2014) Dynamic Pricing of Perishable Assets Under Competition. Management Science 60(5):1248-1250
[23] Manel Baucells, Nikolay Osadchiy, Anton Ovchinnikov (2016) Behavioral Anomalies in Consumer Wait-or-Buy Decisions and Their Implications for Markdown Management. Operations Research,pp.5-9
[24] Omar Besbes, Ilan Lobel (2015) Intertemporal Price Discrimination: Structure and Computation of Optimal Policies. Management Science 61(1):95-100.
[25] Sang-Eun Byun & Brenda Sternquist (2012) Here Today, Gone Tomorrow: Consumer Reactions to Perceived Limited Availability, Journal of Marketing Theory and Practice, 20:2, 225-229
[26] Jaekwon Chung1 and Dong Li2 1 ,2013, " A simulation of the impacts of dynamic price management for perishable foods on retailer performance in the presence of need-driven purchasing consumers", Kookmin University, Seoul, South Korea; and 2 University of Liverpool, Liverpool, UK,pp1180-1183
[27] Aristeidis Theotokis a,∗, Katerina Pramatari b,1, Michael Tsiros c, 2012," Effects of Expiration Date-Based Pricing on Brand Image Perceptions",Journal of Retailing 88 (1, 2012) 80–83
[28] Gérard P. Cachon,2011, "The Value of Fast Fashion: Quick Response, Enhanced Design, and Strategic Consumer Behavior",MANAGEMENT SCIENCE Vol. 57, No. 4, April 2011, pp. 785–787
[29] Yalçın Akçay, Harihara Prasad Natarajan, Susan H. Xu, (2010) Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice. Management Science 56(8):1353-1358.
[30] Felipe Caro, Jérémie Gallien, (2010) Inventory Management of a Fast-Fashion Retail Network. Operations Research 58(2):261-266.
[31] Yuri Levin, Jeff McGill, Mikhail Nediak, (2009) Dynamic Pricing in the Presence of Strategic Consumers and Oligopolistic Competition. Management Science 55(1):37-40
[32] Rui Yin, Yossi Aviv, Amit Pazgal, Christopher S. Tang, (2009) Optimal Markdown Pricing: Implications of Inventory Display Formats in the Presence of Strategic Customers. Management Science 55(8):1395-1397.
[33] Yossi Aviv, Amit Pazgal, (2008) Optimal Pricing of Seasonal Products in the Presence of Forward-Looking Consumers. Manufacturing & Service Operations Management 10(3):345-349.
[34] Xuanming Su,2007, "Intertemporal Pricing with Strategic Customer Behavior", MANAGEMENT SCIENCE ,Vol. 53, No. 5, May 2007, pp. 730–736
[35] Wen Zhao, Yu-Sheng Zheng, (2000) Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous Demand. Management Science 46(3):381-383.
[36] Charles J. Corbett, Xavier de Groote, (2000) A Supplier's Optimal Quantity Discount Policy Under Asymmetric Information. Management Science 46(3):447-448.
[37] Bernard Caillaud, Romain De Nijs (2014) Strategic Loyalty Reward in Dynamic Price Discrimination. Marketing Science 33(5):729-735.
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