电力市场模型的严格和Γ-robust对应:完全竞争和纳什-古诺均衡

IF 3.7 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Operations Research Perspectives Pub Date : 2021-01-01 DOI:10.1016/j.orp.2021.100197
Anja Kramer , Vanessa Krebs , Martin Schmidt
{"title":"电力市场模型的严格和Γ-robust对应:完全竞争和纳什-古诺均衡","authors":"Anja Kramer ,&nbsp;Vanessa Krebs ,&nbsp;Martin Schmidt","doi":"10.1016/j.orp.2021.100197","DOIUrl":null,"url":null,"abstract":"<div><p>This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the <span><math><mi>Γ</mi></math></span>-approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable convex optimization counterparts that have a clear-cut economic interpretation. In the case of perfect competition, this result corresponds to the two classic welfare theorems, which also apply in both considered robust cases that again yield convex robustified problems. Using the mentioned counterparts, we can also prove the existence and, in some cases, uniqueness of robust equilibria. Surprisingly, it turns out that there is no such economic sensible counterpart for the case of <span><math><mi>Γ</mi></math></span>-robustifications of Nash–Cournot models. Thus, an analog of the welfare theorems does not hold in this case. Finally, we provide a computational case study that illustrates the different effects of the combination of economic competition and uncertainty modeling.</p></div>","PeriodicalId":38055,"journal":{"name":"Operations Research Perspectives","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S221471602100018X/pdfft?md5=f8ff7d80da1885286a3c1d4cdb7683e7&pid=1-s2.0-S221471602100018X-main.pdf","citationCount":"13","resultStr":"{\"title\":\"Strictly and Γ-robust counterparts of electricity market models: Perfect competition and Nash–Cournot equilibria\",\"authors\":\"Anja Kramer ,&nbsp;Vanessa Krebs ,&nbsp;Martin Schmidt\",\"doi\":\"10.1016/j.orp.2021.100197\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the <span><math><mi>Γ</mi></math></span>-approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable convex optimization counterparts that have a clear-cut economic interpretation. In the case of perfect competition, this result corresponds to the two classic welfare theorems, which also apply in both considered robust cases that again yield convex robustified problems. Using the mentioned counterparts, we can also prove the existence and, in some cases, uniqueness of robust equilibria. Surprisingly, it turns out that there is no such economic sensible counterpart for the case of <span><math><mi>Γ</mi></math></span>-robustifications of Nash–Cournot models. Thus, an analog of the welfare theorems does not hold in this case. Finally, we provide a computational case study that illustrates the different effects of the combination of economic competition and uncertainty modeling.</p></div>\",\"PeriodicalId\":38055,\"journal\":{\"name\":\"Operations Research Perspectives\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S221471602100018X/pdfft?md5=f8ff7d80da1885286a3c1d4cdb7683e7&pid=1-s2.0-S221471602100018X-main.pdf\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Operations Research Perspectives\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S221471602100018X\",\"RegionNum\":4,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Perspectives","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S221471602100018X","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 13

摘要

本文主要研究电力市场均衡模型的线性互补问题和不确定条件下的优化问题。我们考虑电力市场的完全竞争模型和纳什-古诺模型,并使用严格鲁棒性和Γ-approach来研究它们的鲁棒性。对于经济竞争和鲁棒化的四种组合中的三种,我们推导出具有明确经济解释的算法易于处理的凸优化对偶。在完全竞争的情况下,这个结果对应于两个经典的福利定理,它们也适用于两种被认为是鲁棒的情况,再次产生凸鲁棒问题。利用上述对应物,我们还可以证明鲁棒均衡的存在性,在某些情况下,还可以证明鲁棒均衡的唯一性。令人惊讶的是,在纳什-古诺模型Γ-robustifications的情况下,没有这样一个经济上合理的对应。因此,福利定理的类比在这种情况下不成立。最后,我们提供了一个计算案例研究,说明经济竞争和不确定性模型相结合的不同效果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Strictly and Γ-robust counterparts of electricity market models: Perfect competition and Nash–Cournot equilibria

This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the Γ-approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable convex optimization counterparts that have a clear-cut economic interpretation. In the case of perfect competition, this result corresponds to the two classic welfare theorems, which also apply in both considered robust cases that again yield convex robustified problems. Using the mentioned counterparts, we can also prove the existence and, in some cases, uniqueness of robust equilibria. Surprisingly, it turns out that there is no such economic sensible counterpart for the case of Γ-robustifications of Nash–Cournot models. Thus, an analog of the welfare theorems does not hold in this case. Finally, we provide a computational case study that illustrates the different effects of the combination of economic competition and uncertainty modeling.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Operations Research Perspectives
Operations Research Perspectives Mathematics-Statistics and Probability
CiteScore
6.40
自引率
0.00%
发文量
36
审稿时长
27 days
期刊最新文献
Distributional robustness based on Wasserstein-metric approach for humanitarian logistics problem under road disruptions A generalized behavioral-based goal programming approach for decision-making under imprecision δ-perturbation of bilevel optimization problems: An error bound analysis Competitive pricing and seed node selection in a two-echelon supply chain Strategizing emissions reduction investment for a livestock production farm amid power demand pattern: A path to sustainable growth under the carbon cap environmental regulation
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1