Quadratic stochastic operators and zero-sum game dynamics

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

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	4430/37341
Uncontrolled Keywords:	Quadratic stochastic operators
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Prof. Nasir Ganikhodjaev
Date Deposited:	23 Jul 2014 09:03
Last Modified:	23 Jan 2018 12:04
URI:	http://irep.iium.edu.my/id/eprint/37341

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