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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Main Authors:	Ganikhodjaev, Nasir, Ganikhodjaev, Rasul, Jamilov, Uygun
Format:	Article
Language:	English
Published:	Cambridge University Press 2015
Subjects:	QA Mathematics
Online Access:	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

id	iium-37341
recordtype	eprints
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
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Ganikhodjaev, Nasir Ganikhodjaev, Rasul Jamilov, Uygun Quadratic stochastic operators and zero-sum game dynamics
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.
format	Article
author	Ganikhodjaev, Nasir Ganikhodjaev, Rasul Jamilov, Uygun
author_facet	Ganikhodjaev, Nasir Ganikhodjaev, Rasul Jamilov, Uygun
author_sort	Ganikhodjaev, Nasir
title	Quadratic stochastic operators and zero-sum game dynamics
title_short	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_sort	quadratic stochastic operators and zero-sum game dynamics
publisher	Cambridge University Press
publishDate	2015
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
first_indexed	2023-09-18T20:53:35Z
last_indexed	2023-09-18T20:53:35Z
_version_	1777410156077776896

Quadratic stochastic operators and zero-sum game dynamics

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