具有时变估值的跨期价格歧视
Intertemporal Price Discrimination with Time-Varying Valuations
摘要：
一个销售非易腐产品的公司考虑跨期价格歧视，以最大化其长期平均收益为目标。我们考虑一个一般模型的病人的客户不断变化的估值。到达的顾客等待一个随机但有界的时间长度，当产品价格低于他们的估价时购买产品，这是一个随机过程。我们证明了一类循环策略的最优性，并得到了一个算法，产生它们。当跨期定价的速度被限制为与客户耐心水平的上界相当时，我们可以很好地控制周期长度和优化周期策略的结构。研究结果也适用于前瞻性的战略客户，以及在一个替代目标下，最大限度地提高无限的地平线折扣收入。我们投我们的结果在一个一般的框架，优化长期平均收入的一类收入函数，我们表示{ \it弱耦合}，其中每个周期的收入取决于有限数量的相邻价格。我们详细分析了马尔可夫估值的情况下，我们可以得到封闭形式的收入函数和我们的主要结果的一些改进。我们还扩展我们的结果的情况下，耐心水平，只有在期望的范围内。
英文摘要：
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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