Extended matrix norm method: Applications to bimatrix games and convergence results

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dc.authoridOzkaya, Murat/0000-0001-7241-4710
dc.authoridPerc, Matjaz/0000-0002-3087-541X
dc.contributor.authorIzgi, Burhaneddin
dc.contributor.authorOzkaya, Murat
dc.contributor.authorUre, Nazim Kemal
dc.contributor.authorPerc, Matjaz
dc.date.accessioned2025-01-27T21:13:02Z
dc.date.available2025-01-27T21:13:02Z
dc.date.issued2023
dc.departmentÇanakkale Onsekiz Mart Üniversitesi
dc.description.abstractIn this paper, we extend and apply the Matrix Norm (MN) approach to the nonzero-sum bimatrix games. We present preliminary results regarding the convergence of the MN ap-proaches. We provide a notation for expressing nonzero-sum bimatrix games in terms of two matrix games using the idea of separation of a bimatrix game into two different ma-trix games. Next, we prove theorems regarding boundaries of the game value depending on only norms of the payoff matrix for each player of the nonzero-sum bimatrix game. In ad-dition to these, we refine the boundaries of the game value for the zero/nonzero sum ma-trix games. Therefore, we succeed to find an improved interval for the game value, which is a crucial improvement for both nonzero and zero-sum matrix games. As a consequence, we can solve a nonzero-sum bimatrix game for each player approximately without solving any equations. Moreover, we modify the inequalities for the extrema of the strategy set for the nonzero-sum bimatrix games. Furthermore, we adapt the min-max theorem of the MN approach for the nonzero-sum bimatrix games. Finally, we consider various bimatrix game examples from the literature, including the famous battle of sexes, to demonstrate the consistency of our approaches. We also show that the repeated applications of Ex-tended Matrix Norm (EMN) methods work well to obtain a better-estimated game value in view of the obtained convergence results.(c) 2022 Elsevier Inc. All rights reserved.
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TUBITAK) [121E394]; Slovenian Research Agency [P1-0403, J1-2457]
dc.description.sponsorshipThis work is supported by the Scientific and Technological Research Council of Turkey (in Turkish: TUB. ITAK) under grant agreement 121E394. M.P. is supported by the Slovenian Research Agency (Grant Nos. P1-0403 and J1-2457). The authors would like to thank the anonymous referees and the editor for their valuable suggestions and comments that helped to improve the content of the article.
dc.identifier.doi10.1016/j.amc.2022.127553
dc.identifier.issn0096-3003
dc.identifier.issn1873-5649
dc.identifier.scopus2-s2.0-85138485051
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.amc.2022.127553
dc.identifier.urihttps://hdl.handle.net/20.500.12428/28254
dc.identifier.volume438
dc.identifier.wosWOS:000862771000003
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier Science Inc
dc.relation.ispartofApplied Mathematics and Computation
dc.relation.publicationcategoryinfo:eu-repo/semantics/openAccess
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20250125
dc.subjectGame theory
dc.subjectNonzero sum game
dc.subjectBimatrix game
dc.subjectMatrix norms
dc.subjectBattle of sexes
dc.subjectConvergence
dc.titleExtended matrix norm method: Applications to bimatrix games and convergence results
dc.typeArticle

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