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A generalization of the increasing generalized failure rate unimodality condition
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Leonardos, Stefanos, Koki, Constandina and Melolidakis, Costis (2023) A generalization of the increasing generalized failure rate unimodality condition. Annals of Operations Research . doi:10.1007/s10479-023-05425-z ISSN 0254-5330.
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Official URL: http://doi.org/10.1007/s10479-023-05425-z
Abstract
In this paper, we study unimodality conditions for distributions that describe markets with stochastic demand. Such conditions naturally emerge in the analysis of game-theoretic models of market competition (Cournot games) and supply chain coordination (Stackelberg games). We express the price elasticity of expected demand in terms of the mean residual life (MRL) function of the demand distribution and characterize optimal prices or equivalently, points of unitary elasticity, as fixed points of the MRL function. This leads to economic interpretable conditions on the demand distribution under which such fixed points exist and are unique. We find that markets with increasing price elasticity of expected demand that eventually become elastic correspond to distributions with decreasing generalized mean residual life (DGMRL) and finite second moment. DGMRL distributions strictly generalize the widely used increasing generalized failure rate (IGFR) distributions. We further elaborate on the relationship of the two classes, link their limiting behavior at infinity and examine moment and closure properties of DGMRL distributions that are important in economic applications. The DGMRL unimodality condition is useful in the analysis of optimal decisions under uncertainty in settings that are not covered by the widely-used IGFR condition; thus, it can be of broader interest to the game-theory and operations research literature.
| Item Type: | Journal Article | ||||||||
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| Subjects: | H Social Sciences > HB Economic Theory | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Demand (Economic theory), Prices, Competition, Business logistics | ||||||||
| Journal or Publication Title: | Annals of Operations Research | ||||||||
| Publisher: | Springer New York LLC | ||||||||
| ISSN: | 0254-5330 | ||||||||
| Official Date: | 2023 | ||||||||
| Dates: |
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| DOI: | 10.1007/s10479-023-05425-z | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 4 August 2023 | ||||||||
| Date of first compliant Open Access: | 4 August 2023 | ||||||||
| RIOXX Funder/Project Grant: |
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