A firm that sells a non perishable product considers intertemporal price discrimination in the objective of maximizing the long-run average revenue. Each period, a number of interested customers approach the firm and can either purchase on arrival, or remain in the system for a period of time. During this time, each customer's valuation changes following a discrete and homogenous Markov chain. Customers leave the system if they either purchase at some point, or their valuations reach an absorbing state v0. We show that, in this context, cyclic strategies are optimal, or nearly optimal. When the pace of intertemporal pricing is constrained to be comparable to customers patience level, we have a good control on the cycle length and on the structure of the optimizing cyclic policies. We also obtain an algorithm that yields the optimal (or near optimal) cyclic solutions in polynomial time in the number of prices. We cast part of our results in a general framework of optimizing the long-run average revenues for a class of payoffs that we call weakly coupled, in which the revenue per period depends on a finite number of neighboring prices.

中文翻译：

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时变价格的跨期价格歧视

销售不易腐烂产品的公司会考虑跨期价格歧视，目的是最大化长期平均收入。在每个时期，许多感兴趣的客户都会联系公司，并可以在到达时进行购买，或者在系统中保留一段时间。在此期间，每个客户的估价都遵循离散且同质的马尔可夫链。如果客户在某个时候购买或他们的估值达到吸收状态v0，则他们离开系统。我们表明，在这种情况下，循环策略是最优的或接近最优的。当跨期定价的步伐被限制为与客户的耐心水平可比时，我们就可以很好地控制周期长度和优化周期政策的结构。我们还获得了一种算法，该算法可在价格数量的多项式时间内产生最佳（或接近最佳）循环解。我们将部分结果放到针对所谓的弱耦合收益类别优化长期平均收益的通用框架中，其中每个期间的收益取决于有限数量的邻近价格。