| Title: | Extended matrix norm method : applications to bimatrix games and convergence results |
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| Authors: | ID İzgi, Burhaneddin (Author)
ID Özkaya, Murat (Author)
ID Üre, Nazım Kemal (Author)
ID Perc, Matjaž (Author) |
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| Files: |  RAZ_İzgi_Burhaneddin_2023.pdf (838,66 KB)
MD5: 0F66906C44551F8C312066263649FED0
 https://doi.org/10.1016/j.amc.2022.127553
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | In 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 approaches. 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 matrix 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 addition to these, we refine the boundaries of the game value for the zero/nonzero sum matrix 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 Extended Matrix Norm (EMN) methods work well to obtain a better-estimated game value in view of the obtained convergence results. |
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| Keywords: | game theory, nonzero sum game, bimatrix game, matrix norms, battle of sexes, convergence |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 26.07.2022 |
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| Article acceptance date: | 14.09.2022 |
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| Publication date: | 26.09.2022 |
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| Publisher: | Elsevier |
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| Year of publishing: | 2023 |
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| Number of pages: | str. 1-11 |
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| Numbering: | Vol. 438 |
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| PID: | 20.500.12556/DKUM-88112  |
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| UDC: | 53:519.83 |
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| ISSN on article: | 0096-3003 |
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| COBISS.SI-ID: | 123701251 |
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| DOI: | 10.1016/j.amc.2022.127553 |
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| Publication date in DKUM: | 15.04.2024 |
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| Views: | 632 |
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| Downloads: | 338 |
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| Metadata: |    |
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| Categories: | Misc.
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