Tight bounds on the relative performances of pricing optimization mechanisms in storable good markets

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Gerardo Berbeglia , Shant Boodaghians , Adrian Vetta
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引用次数: 0

Abstract

In the storable good monopoly problem, a monopolist sells a storable good by announcing a price in each time period. Each consumer has a unitary demand per time period with an arbitrary valuation. In each period, consumers may buy none, one, or more than one good (in which case the extra goods are stored for future consumption incurring in a linear storage cost). We compare the performance of two important monopoly pricing optimization mechanisms: price optimization using pre-announced prices and price optimization without commitments (contingent mechanism). In pre-announced pricing the prices in each time period are stated in advance; in a price contingent mechanism each price is stated at the start of the time period, and these prices are dependent upon past purchases. We prove that monopolist can earn up to O(logT+logN) times more profit by using a pre-announced pricing mechanism rather than a price contingent mechanism. Here T denotes the number of time periods and N denotes the number of consumers. This bound is tight; examples exist where the monopolist would earn a factor Ω(logT+logN) more by using a pre-announced pricing mechanism.

仓储商品市场中定价优化机制相对性能的严格限制
在可储存商品垄断问题中,垄断者通过在每个时间段公布价格来销售可储存商品。每个消费者在每个时间段都有一个统一的需求和一个任意的估值。在每一个时期,消费者可能不购买,也可能购买一种或多种商品(在这种情况下,多余的商品被储存起来以备将来消费,从而产生线性存储成本)。我们比较了两种重要的垄断定价优化机制的表现:使用预先宣布价格的价格优化和没有承诺的价格优化(偶然机制)。预公告定价是指在每一时段内的价格预先列明;在价格或有机制中,每个价格都是在时间段开始时确定的,这些价格取决于过去的购买情况。我们证明了通过使用预先宣布的定价机制而不是价格偶然机制,垄断者可以获得高达O(logT+logN)倍的利润。这里T表示时间段的数量,N表示消费者的数量。这个界限很紧;存在这样的例子,垄断者可以通过使用预先宣布的定价机制赚取Ω(logT+logN)更多。
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来源期刊
Discrete Optimization
Discrete Optimization 管理科学-应用数学
CiteScore
2.10
自引率
9.10%
发文量
30
审稿时长
>12 weeks
期刊介绍: Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.
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