Mather sets of a cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies
UDC 517.9 We establish conditions under which a two-dimensional cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies, is determined by a twist mapping of the plane. For the indicated cascade, we prove the existence of Mather sets corresponding to the rotation nu...
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| Datum: | 2026 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9034 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.9
We establish conditions under which a two-dimensional cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies, is determined by a twist mapping of the plane. For the indicated cascade, we prove the existence of Mather sets corresponding to the rotation numbers from a certain interval. In this way, we explain why, in the computer experiments, the orbits of the analyzed cascade are located on closed curves and, in a certain sense, have the property of local convexity. |
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| DOI: | 10.3842/umzh.v77i6.9034 |