论文标题

跨时价歧视与时变估值

Intertemporal Price Discrimination with Time-Varying Valuations

论文作者

Victor, Araman, Bassam, Fayad

论文摘要

一家出售不可腐烂产品的公司认为,跨期价格歧视的目的是最大化其长期平均收入。我们考虑了具有不断变化的估值的患者客户的一般模型。到达客户等待随机但有限的时间,并在其价格低于其估值时购买该产品,该产品在随机过程之后变化。我们展示了一类环状策略的最佳性,并获得了产生它们的算法。当跨期定价的速度被限制在与客户耐心水平上的上限相当时,我们可以很好地控制周期长度和优化循环策略的结构。结果也适用于前瞻性战略客户以及最大化无限范围折扣收入的另一种目标。 我们将结果投入了一个一般框架,该框架优化了一类收入功能的长期平均收入,我们表示{\ nit弱耦合},其中每个时期的收入取决于相邻价格的有限数量。我们详细分析了马尔可夫估值的情况,在该情况下,我们可以获得收入功能的封闭形式公式以及我们主要结果的一些改进。我们还将结果扩展到仅在预期中才有限制的耐心水平的情况。

A firm that sells a non perishable product considers intertemporal price discrimination in the objective of maximizing its long-run average revenue. We consider a general model of patient customers with changing valuations. Arriving customers wait for a random but bounded length of time and purchase the product when its price falls below their valuation, which varies following a stochastic process. We show the optimality of a class of cyclic strategies and obtain an algorithm that yields them. When the pace of intertemporal pricing is constrained to be comparable to the upper bound on customers patience levels, we have a good control on the cycle length and on the structure of the optimizing cyclic policies. The results also hold for forward looking strategic customers as well as under an alternative objective of maximizing infinite horizon discounted revenue. We cast our results in a general framework of optimizing the long-run average revenue for a class of revenue functions that we denote {\it weakly coupled}, in which the revenue per period depends on a finite number of neighboring prices. We analyze in detail the case of Markovian valuations where we can obtain closed form formulations of the revenue function and some refinements of our main results. We also extend our results to the case of patience levels that are bounded only in expectation.

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