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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| Date: | 2026 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9034 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513358404386816 |
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| author | Kolner, V. Parasyuk, I. Кольнер, Вікторія Парасюк, Ігор Парасюк, Ігор |
| author_facet | Kolner, V. Parasyuk, I. Кольнер, Вікторія Парасюк, Ігор Парасюк, Ігор |
| author_sort | Kolner, V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-22T13:31:27Z |
| description | 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. |
| doi_str_mv | 10.3842/umzh.v77i6.9034 |
| first_indexed | 2026-03-24T03:43:25Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-9034 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T03:43:25Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/2e/338d253916532febce6e28d213dba22e |
| spelling | umjimathkievua-article-90342026-03-22T13:31:27Z Mather sets of a cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies Множини Мазера каскаду, породженого FTRL-алгоритмом двоагентної гри з нульовою сумою та мішаними стратегіями Kolner, V. Parasyuk, I. Кольнер, Вікторія Парасюк, Ігор Парасюк, Ігор cascade FTRL algorithm monotone twist mapping Mather set каскад FTRL-алгоритм монотонне крутне відображення множина Мазера 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. УДК 517.9 Встановлено умови, за яких двовимірний каскад, породжений FTRL-алгоритмом двоагентної гри з нульовою сумою та мішаними стратегіями, визначається крутним відображенням площини. Для зазначеного каскаду доведено існування множин Мазера, що відповідають числам обертання з певного інтервалу. У такий спосіб пояснено, чому в комп'ютерних експериментах орбіти каскаду розташовуються на замкнених кривих і в певному сенсі мають властивість локальної опуклості. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9034 10.3842/umzh.v77i6.9034 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 6 (2025); 405–425 Український математичний журнал; Том 77 № 6 (2025); 405–425 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/9034/10543 Copyright (c) 2025 V. Kolner, I. Parasyuk |
| spellingShingle | Kolner, V. Parasyuk, I. Кольнер, Вікторія Парасюк, Ігор Парасюк, Ігор Mather sets of a cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies |
| title | Mather sets of a cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies |
| title_alt | Множини Мазера каскаду, породженого FTRL-алгоритмом двоагентної гри з нульовою сумою та мішаними стратегіями |
| title_full | Mather sets of a cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies |
| title_fullStr | Mather sets of a cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies |
| title_full_unstemmed | Mather sets of a cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies |
| title_short | Mather sets of a cascade generated by the FTRL algorithm of a two-agent zero-sum game with mixed strategies |
| title_sort | mather sets of a cascade generated by the ftrl algorithm of a two-agent zero-sum game with mixed strategies |
| topic_facet | cascade FTRL algorithm monotone twist mapping Mather set каскад FTRL-алгоритм монотонне крутне відображення множина Мазера |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9034 |
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