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Article: On Nash–Stackelberg–Nash games under decision-dependent uncertainties: Model and equilibrium

TitleOn Nash–Stackelberg–Nash games under decision-dependent uncertainties: Model and equilibrium
Authors
KeywordsDecision-dependent uncertainties
Existence
Nash equilibrium
Nash–Stackelberg–Nash game
Issue Date1-Aug-2022
PublisherElsevier
Citation
Automatica, 2022, v. 142 How to Cite?
Abstract

In this paper, we discuss a class of two-stage hierarchical games with multiple leaders and followers, which is called Nash–Stackelberg–Nash (N–S–N) games. Particularly, we consider N–S–N games under decision-dependent uncertainties (DDUs). DDUs refer to the uncertainties that are affected by the strategies of decision-makers and have been rarely addressed in game equilibrium analysis. In this paper, we first formulate the N–S–N games with DDUs of complete ignorance, where the interactions between the players and DDUs are characterized by uncertainty sets that depend parametrically on the players’ strategies. Then, a rigorous definition for the equilibrium of the game is established by consolidating generalized Nash equilibrium and Pareto-Nash equilibrium. Afterward, we prove the existence of the equilibrium of N–S–N games under DDUs by applying Kakutani's fixed-point theorem. Finally, an illustrative example is provided to show the impact of DDUs on the equilibrium of N–S–N games.


Persistent Identifierhttp://hdl.handle.net/10722/338415
ISSN
2023 Impact Factor: 4.8
2023 SCImago Journal Rankings: 3.502
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorZhang, Yunfan-
dc.contributor.authorLiu, Feng-
dc.contributor.authorWang, Zhaojian-
dc.contributor.authorChen, Yue-
dc.contributor.authorFeng, Shuanglei-
dc.contributor.authorWu, Qiuwei-
dc.contributor.authorHou, Yunhe-
dc.date.accessioned2024-03-11T10:28:40Z-
dc.date.available2024-03-11T10:28:40Z-
dc.date.issued2022-08-01-
dc.identifier.citationAutomatica, 2022, v. 142-
dc.identifier.issn0005-1098-
dc.identifier.urihttp://hdl.handle.net/10722/338415-
dc.description.abstract<p>In this paper, we discuss a class of two-stage hierarchical games with multiple leaders and followers, which is called Nash–Stackelberg–Nash (N–S–N) games. Particularly, we consider N–S–N games under decision-dependent uncertainties (DDUs). DDUs refer to the uncertainties that are affected by the strategies of decision-makers and have been rarely addressed in game equilibrium analysis. In this paper, we first formulate the N–S–N games with DDUs of complete ignorance, where the interactions between the players and DDUs are characterized by uncertainty sets that depend parametrically on the players’ strategies. Then, a rigorous definition for the equilibrium of the game is established by consolidating generalized Nash equilibrium and Pareto-Nash equilibrium. Afterward, we prove the existence of the equilibrium of N–S–N games under DDUs by applying Kakutani's fixed-point theorem. Finally, an illustrative example is provided to show the impact of DDUs on the equilibrium of N–S–N games.</p>-
dc.languageeng-
dc.publisherElsevier-
dc.relation.ispartofAutomatica-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectDecision-dependent uncertainties-
dc.subjectExistence-
dc.subjectNash equilibrium-
dc.subjectNash–Stackelberg–Nash game-
dc.titleOn Nash–Stackelberg–Nash games under decision-dependent uncertainties: Model and equilibrium-
dc.typeArticle-
dc.identifier.doi10.1016/j.automatica.2022.110401-
dc.identifier.scopuseid_2-s2.0-85130935358-
dc.identifier.volume142-
dc.identifier.eissn1873-2836-
dc.identifier.isiWOS:000833419800005-
dc.identifier.issnl0005-1098-

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