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dc.contributor.authorZhang, M.
dc.contributor.authorSun, Jie
dc.contributor.authorXu, Honglei
dc.date.accessioned2023-04-16T10:19:53Z
dc.date.available2023-04-16T10:19:53Z
dc.date.issued2019
dc.identifier.citationZhang, M. and Sun, J. and Xu, H. 2019. Two-stage quadratic games under uncertainty and their solution by progressive hedging algorithms. SIAM Journal on Optimization. 29 (3): pp. 1799-1818.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/91438
dc.identifier.doi10.1137/17M1151067
dc.description.abstract

A model of a two-stage N-person noncooperative game under uncertainty is studied, in which at the first stage each player solves a quadratic program parameterized by other players’ decisions and then at the second stage the player solves a recourse quadratic program parameterized by the realization of a random vector, the second-stage decisions of other players, and the first-stage decisions of all players. The problem of finding a Nash equilibrium of this game is shown to be equivalent to a stochastic linear complementarity problem. A linearly convergent progressive hedging algorithm is proposed for finding a Nash equilibrium if the resulting complementarity problem is monotone. For the nonmonotone case, it is shown that, as long as the complementarity problem satisfies an additional elicitability condition, the progressive hedging algorithm can be modified to find a local Nash equilibrium at a linear rate. The elicitability condition is reminiscent of the sufficient second-order optimality condition in nonlinear programming. Various numerical experiments indicate that the progressive hedging algorithms are efficient for mid-sized problems. In particular, the numerical results include a comparison with the best response method that is commonly adopted in the literature.

dc.languageEnglish
dc.publisherSIAM PUBLICATIONS
dc.relation.sponsoredbyhttp://purl.org/au-research/grants/arc/DP160102819
dc.subjectScience & Technology
dc.subjectPhysical Sciences
dc.subjectMathematics, Applied
dc.subjectMathematics
dc.subjectmultistage noncooperative game under uncertainty
dc.subjectprogressive hedging algorithm
dc.subjectstochastic linear complementarity problem
dc.subjectstochastic variational inequality
dc.titleTwo-stage quadratic games under uncertainty and their solution by progressive hedging algorithms
dc.typeJournal Article
dcterms.source.volume29
dcterms.source.number3
dcterms.source.startPage1799
dcterms.source.endPage1818
dcterms.source.issn1052-6234
dcterms.source.titleSIAM Journal on Optimization
dc.date.updated2023-04-16T10:19:53Z
curtin.departmentSchool of Elec Eng, Comp and Math Sci (EECMS)
curtin.accessStatusOpen access
curtin.facultyFaculty of Science and Engineering
curtin.contributor.orcidSun, Jie [0000-0001-5611-1672]
curtin.contributor.orcidXu, Honglei [0000-0003-3212-2080]
curtin.contributor.researcheridSun, Jie [B-7926-2016] [G-3522-2010]
curtin.contributor.researcheridXu, Honglei [A-1307-2010]
dcterms.source.eissn1095-7189
curtin.contributor.scopusauthoridSun, Jie [16312754600] [57190212842]
curtin.contributor.scopusauthoridXu, Honglei [23037699600] [57203334243] [57203334253]
curtin.repositoryagreementV3


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