Gerardo Berbeglia , Shant Boodaghians , Adrian Vetta
{"title":"Tight bounds on the relative performances of pricing optimization mechanisms in storable good markets","authors":"Gerardo Berbeglia , Shant Boodaghians , Adrian Vetta","doi":"10.1016/j.disopt.2021.100671","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mo>log</mo><mi>T</mi><mo>+</mo><mo>log</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> times more profit by using a pre-announced pricing mechanism rather than a price contingent mechanism. Here <span><math><mi>T</mi></math></span><span> denotes the number of time periods and </span><span><math><mi>N</mi></math></span> denotes the number of consumers. This bound is tight; examples exist where the monopolist would earn a factor <span><math><mrow><mi>Ω</mi><mrow><mo>(</mo><mo>log</mo><mi>T</mi><mo>+</mo><mo>log</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> more by using a pre-announced pricing mechanism.</p></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Optimization","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572528621000505","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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 times more profit by using a pre-announced pricing mechanism rather than a price contingent mechanism. Here denotes the number of time periods and denotes the number of consumers. This bound is tight; examples exist where the monopolist would earn a factor more by using a pre-announced pricing mechanism.
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.