Quadratic stochastic operators and zero-sum game dynamics
In this paper we consider the set of all extremal Volterra quadratic stochastic operators defined on a unit simplex S4 and show that such operators can be reinterpreted in terms of zero-sum games. We show that an extremal Volterra operator is non-ergodic and an appropriate zero-sum game is a rock-pa...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2015
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| Online Access: | http://irep.iium.edu.my/37341/ http://irep.iium.edu.my/37341/1/37341.pdf |
| _version_ | 1848781397722923008 |
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| author | Ganikhodjaev, Nasir Ganikhodjaev, Rasul Jamilov, Uygun |
| author_facet | Ganikhodjaev, Nasir Ganikhodjaev, Rasul Jamilov, Uygun |
| author_sort | Ganikhodjaev, Nasir |
| building | IIUM Repository |
| collection | Online Access |
| description | In this paper we consider the set of all extremal Volterra quadratic stochastic operators defined on a unit simplex S4 and show that such operators can be reinterpreted in terms of zero-sum games. We show that an extremal Volterra operator is non-ergodic and an appropriate zero-sum game is a rock-paper-scissors game if either the Volterra operator is a uniform operator or for a non-uniform Volterra operator V there exists a subset I⊂{1,2,3,4,5} with |I|⩽2 such that ∑i∈I(Vnx)i→0, and the restriction of V on an invariant face ΓI={x∈Sm−1:xi=0,i∈I} is a uniform Volterra operator. |
| first_indexed | 2025-11-14T15:48:55Z |
| format | Article |
| id | iium-37341 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T15:48:55Z |
| publishDate | 2015 |
| publisher | Cambridge University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-373412018-01-23T04:04:45Z http://irep.iium.edu.my/37341/ Quadratic stochastic operators and zero-sum game dynamics Ganikhodjaev, Nasir Ganikhodjaev, Rasul Jamilov, Uygun QA Mathematics In this paper we consider the set of all extremal Volterra quadratic stochastic operators defined on a unit simplex S4 and show that such operators can be reinterpreted in terms of zero-sum games. We show that an extremal Volterra operator is non-ergodic and an appropriate zero-sum game is a rock-paper-scissors game if either the Volterra operator is a uniform operator or for a non-uniform Volterra operator V there exists a subset I⊂{1,2,3,4,5} with |I|⩽2 such that ∑i∈I(Vnx)i→0, and the restriction of V on an invariant face ΓI={x∈Sm−1:xi=0,i∈I} is a uniform Volterra operator. Cambridge University Press 2015-08 Article PeerReviewed application/pdf en http://irep.iium.edu.my/37341/1/37341.pdf Ganikhodjaev, Nasir and Ganikhodjaev, Rasul and Jamilov, Uygun (2015) Quadratic stochastic operators and zero-sum game dynamics. Ergodic Theory and Dynamical Systems, 35 (5). pp. 1443-1473. ISSN 0143-3857 http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9805901 10.1017/etds.2013.109 |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Ganikhodjaev, Rasul Jamilov, Uygun Quadratic stochastic operators and zero-sum game dynamics |
| title | Quadratic stochastic operators and zero-sum game dynamics |
| title_full | Quadratic stochastic operators and zero-sum game dynamics |
| title_fullStr | Quadratic stochastic operators and zero-sum game dynamics |
| title_full_unstemmed | Quadratic stochastic operators and zero-sum game dynamics |
| title_short | Quadratic stochastic operators and zero-sum game dynamics |
| title_sort | quadratic stochastic operators and zero-sum game dynamics |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/37341/ http://irep.iium.edu.my/37341/ http://irep.iium.edu.my/37341/ http://irep.iium.edu.my/37341/1/37341.pdf |