Markov Games with Several Ergodic Classes
We consider Markov games of the general form characterized by the property that, for all stationary strategies of players, the set of game states is partitioned into several ergodic sets and a transient set, which may vary depending on the strategies of players. As a criterion, we choose the mean pa...
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| Date: | 2003 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3951 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510083793813504 |
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| author | Ibragimov, G. I. Ибрагимов, Г. И. Ибрагимов, Г. И. |
| author_facet | Ibragimov, G. I. Ибрагимов, Г. И. Ибрагимов, Г. И. |
| author_sort | Ibragimov, G. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:16:01Z |
| description | We consider Markov games of the general form characterized by the property that, for all stationary strategies of players, the set of game states is partitioned into several ergodic sets and a transient set, which may vary depending on the strategies of players. As a criterion, we choose the mean payoff of the first player per unit time. It is proved that the general Markov game with a finite set of states and decisions of both players has a value, and both players have ε-optimal stationary strategies. The correctness of this statement is demonstrated on the well-known Blackwell's example (“Big Match”). |
| first_indexed | 2026-03-24T02:51:22Z |
| format | Article |
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| id | umjimathkievua-article-3951 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:51:22Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ea/affc08de4b8c41f5484370088a091fea.pdf |
| spelling | umjimathkievua-article-39512020-03-18T20:16:01Z Markov Games with Several Ergodic Classes Марковские игры с несколькими эргодическими классами Ibragimov, G. I. Ибрагимов, Г. И. Ибрагимов, Г. И. We consider Markov games of the general form characterized by the property that, for all stationary strategies of players, the set of game states is partitioned into several ergodic sets and a transient set, which may vary depending on the strategies of players. As a criterion, we choose the mean payoff of the first player per unit time. It is proved that the general Markov game with a finite set of states and decisions of both players has a value, and both players have ε-optimal stationary strategies. The correctness of this statement is demonstrated on the well-known Blackwell's example (“Big Match”). Розглянуто марковські ігри загального вигляду, які характеризуються тим, що при будь-яких стаціонарних стратегіях гравців множина станів гри розбивається на декілька ергодичних множин і незворотну множину, що можуть змінюва тися в залежност і від стратегії гравців. За критерій вибрано середній виграш першого гравця за одиницю часу. Доведено, що загальна мар-ковська гра із скінченною множиною станів і розв'язків обох гравців має значення, а обидва гравці мають ε-оптималміі стаціонарні стратегії. Справедливість цього твердження продемонстровано на прикладі Блекуелла — „великий матч". Institute of Mathematics, NAS of Ukraine 2003-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3951 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 6 (2003); 762-778 Український математичний журнал; Том 55 № 6 (2003); 762-778 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3951/4615 https://umj.imath.kiev.ua/index.php/umj/article/view/3951/4616 Copyright (c) 2003 Ibragimov G. I. |
| spellingShingle | Ibragimov, G. I. Ибрагимов, Г. И. Ибрагимов, Г. И. Markov Games with Several Ergodic Classes |
| title | Markov Games with Several Ergodic Classes |
| title_alt | Марковские игры с несколькими эргодическими классами |
| title_full | Markov Games with Several Ergodic Classes |
| title_fullStr | Markov Games with Several Ergodic Classes |
| title_full_unstemmed | Markov Games with Several Ergodic Classes |
| title_short | Markov Games with Several Ergodic Classes |
| title_sort | markov games with several ergodic classes |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3951 |
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